Image encoding apparatus and image decoding apparatus

ABSTRACT

According to one embodiment, an image encoding apparatus includes a setting unit configured to set a combination of a vertical transform matrix and a horizontal transform matrix corresponding to the target image. The combination includes any of a plurality of transform matrices including a first transform matrix and a second transform matrix which increases a coefficient density compared to the first transform matrix if a one-dimensional orthogonal transformation in a direction orthogonal to a line of a group of reference pixels on at least one line is performed on the prediction error in the intra-prediction mode in which the group of reference pixels is referenced to generate an intra-prediction image.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation Application of PCT Application No.PCT/JP2010/062007, filed Jul. 15, 2010, the entire contents of which areincorporated herein by reference.

FIELD

Embodiments described herein relate generally to orthogonaltransformation and inverse orthogonal transformation in encoding anddecoding of videos.

BACKGROUND

In recent years, an image coding method with significantly improvedcoding efficiency has been jointly recommended by ITU-T and ISO/IEC asITU-T REC. H.264 and ISO/IEC 14496-10 (hereinafter referred as “H.264”).H.264 carries out discrete cosine transformation (DCT) and inversediscrete cosine transformation (IDCT) as orthogonal transformation andinverse orthogonal transformation on prediction errors in a target pixelblock regardless of a prediction scheme applied to the target pixelblock.

Extended H.264 is expected to carry out orthogonal transformation andinverse orthogonal transformation using individual transform bases forthe respective nine types of prediction modes specified forintra-picture prediction (intra-prediction), thus improving the codingefficiency.

However, it is difficult, in connection with implementation, to carryout orthogonal transformation and inverse orthogonal transformationusing individual transform bases for the respective plural types ofprediction modes. For example, hardware implementation requires not onlydedicated hardware for DCT and IDCT required for H.264 but alsodedicated hardware for individual orthogonal transformations and inverseorthogonal transformations for the respective plural types of predictiondirections. The addition of the dedicated hardware increases the scaleof relevant circuits.

Software implementation enables not only DCT matrices but alsoindividual transform matrices for the respective types of predictiondirections to be loaded from a memory as appropriate and held in a cachememory as appropriate. In this case, the desired orthogonaltransformation and inverse orthogonal transformation can be implementedby a general-purpose multiplier. However, disadvantageously, costsincrease as a result of an increase in memory bandwidth or in cachememory size.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating an image encoding apparatusaccording to a first embodiment.

FIG. 2 is a block diagram illustrating an orthogonal transformation unitaccording to the first embodiment.

FIG. 3 is a block diagram illustrating an inverse orthogonaltransformation unit according to the first embodiment.

FIG. 4A is a table illustrating the correspondence between predictionmodes and a vertical transform index and a horizontal transform indexaccording to the first embodiment.

FIG. 4B is a table illustrating the correspondence between the verticaltransform index and 1D transform matrices according to the firstembodiment.

FIG. 4C is a table illustrating the correspondence between thehorizontal transform index and 1D transform matrices according to thefirst embodiment.

FIG. 4D is a table illustrating the correspondence between a transformindex and the vertical transform index and the horizontal transformindex according to the first embodiment.

FIG. 4E is a table obtained by integrating FIG. 4A with FIG. 4D.

FIG. 5A is a block diagram illustrating a coefficient order control unitaccording to the first embodiment.

FIG. 5B is a block diagram illustrating the coefficient order controlunit according to the first embodiment.

FIG. 6A is a diagram illustrating the order of predictive coding of apixel block.

FIG. 6B is a diagram illustrating an example of a pixel block size.

FIG. 6C is a diagram illustrating another example of the pixel blocksize.

FIG. 6D is a diagram illustrating another example of the pixel blocksize.

FIG. 7A is a diagram illustrating an intra-prediction mode.

FIG. 7B is a diagram illustrating the arrangement relation betweenprediction target pixels and reference pixels.

FIG. 7C is a diagram illustrating an intra-prediction mode 1.

FIG. 7D is a diagram illustrating an intra-prediction mode 4.

FIG. 8A is a diagram illustrating a zigzag scan.

FIG. 8B is a diagram illustrating the zigzag scan.

FIG. 8C is a table showing a 2D-1D transformation utilizing the zigzagscan.

FIG. 9 is a table illustrating individual 2D-1D transformations for therespective prediction modes.

FIG. 10A is a flowchart illustrating processing carried out on a codingtarget block by the image encoding apparatus in FIG. 1.

FIG. 10B is a flowchart illustrating the processing carried out on thecoding target block by the image encoding apparatus in FIG. 1.

FIG. 11 is a diagram illustrating a syntax structure.

FIG. 12 is a diagram illustrating slice header syntax.

FIG. 13 is a diagram illustrating coding tree unit syntax.

FIG. 14 is a diagram illustrating transform unit syntax.

FIG. 15 is a block diagram illustrating an orthogonal transformationunit which carries out orthogonal transformation on each of nine typesof prediction directions using a particular transform basis.

FIG. 16 is a block diagram illustrating an orthogonal transformationunit according to a second embodiment.

FIG. 17 is a block diagram illustrating an inverse orthogonaltransformation unit according to the second embodiment.

FIG. 18A is a table illustrating the correspondence between theprediction modes and the vertical transform index and the horizontaltransform index according to the second embodiment.

FIG. 18B is a table illustrating the correspondence between the verticaltransform index and 1D transform matrices according to the secondembodiment.

FIG. 18C is a table illustrating the correspondence between thehorizontal transform index and 1D transform matrices according to thesecond embodiment.

FIG. 18D is a table illustrating the correspondence between thetransform index and the vertical transform index and the horizontaltransform index according to the second embodiment.

FIG. 18E is a table obtained by integrating FIG. 18A with FIG. 18D.

FIG. 19 is a block diagram illustrating an orthogonal transformationunit according to a third embodiment.

FIG. 20 is a block diagram illustrating an inverse orthogonaltransformation unit according to the third embodiment.

FIG. 21A is a table illustrating the correspondence between theprediction modes and the vertical transform index and the horizontaltransform index according to the third embodiment.

FIG. 21B is a table illustrating the correspondence between the verticaltransform index and 1D transform matrices according to the thirdembodiment.

FIG. 21C is a table illustrating the correspondence between thehorizontal transform index and 1D transform matrices according to thethird embodiment.

FIG. 21D is a table illustrating the correspondence between thetransform index and the vertical transform index and the horizontaltransform index according to the third embodiment.

FIG. 21E is a table obtained by integrating FIG. 21A with FIG. 21D.

FIG. 22 is a block diagram illustrating an image decoding apparatusaccording to a fourth embodiment.

FIG. 23A is a block diagram illustrating a coefficient order controlunit according to the fourth embodiment.

FIG. 23B is a block diagram illustrating a coefficient order controlunit according to the fourth embodiment.

DETAILED DESCRIPTION

Embodiments will be described below with reference to the drawings.

In general, according to one embodiment, an image encoding apparatusincludes an intra-prediction unit, a setting unit, a first transformingunit and an encoding unit. The intra-prediction unit predicts aprediction error of a target image to be encoded based on anintra-prediction mode. The setting unit sets a combination of a verticaltransform matrix and a horizontal transform matrix corresponding to thetarget image based on a predetermined relation. The first transformingunit transforms the prediction error using the combination of thevertical transform matrix and the horizontal transform matrix, to obtaintransform coefficients. The encoding unit encodes the transformcoefficients and information indicating the intra-prediction mode forthe target image. The combination includes any of a plurality oftransform matrices including a first transform matrix and a secondtransform matrix which increases a coefficient density compared to thefirst transform matrix if a one-dimensional orthogonal transformation ina direction orthogonal to a line of a group of reference pixels on atleast one line is performed on the prediction error in theintra-prediction mode in which the group of reference pixels isreferenced to generate an intra-prediction image.

In the description below, the term “image” may be replaced with the term“image signal”, “image data”, or the like as appropriate.

First Embodiment

A first embodiment relates to an image encoding apparatus. An imagedecoding apparatus corresponding to the image encoding apparatusaccording to the present embodiment will be described in a fourthembodiment. The image encoding apparatus can be implemented by hardwaresuch as LSI (Large-Scale Integration) chips, DSPs (Digital SignalProcessors), FPGAs (Field Programmable Gate Arrays), and the like.Furthermore, the image encoding apparatus can also be implemented byallowing a computer to execute an image encoding program.

As shown in FIG. 1, the image encoding apparatus according to thepresent embodiment includes a subtraction unit 101, an orthogonaltransformation unit 102, a quantization unit 103, a de-quantization unit104, an inverse orthogonal transformation unit 105, an addition unit106, a reference image memory 107, an intra-prediction unit 108, aninter-prediction unit 109, a prediction selection unit 110, a predictionselection switch 111, a 1D (one-dimensional) transformation matrix setunit 112, a coefficient order control unit 113, an entropy encoding unit114, an output buffer 115, and an encoding control unit 116.

The image encoding apparatus in FIG. 1 divides each of the frame orfields forming an input image 118 into a plurality of pixel blocks,carries out predictive coding on the pixel blocks resulting from thedivision, and outputs encoded data 130. For simplification, predictivecoding is hereinafter assumed to be carried out on a pixel block fromupper left to lower right as shown in FIG. 6A. FIG. 6A shows a codingtarget frame f in which an encoded pixel blocks p are positioned to theleft of and above a coding target pixel block c.

Here, the pixel block refers to, for example, a coding tree unit, amacro block, a sub-block, or a pixel. The pixel block is hereinafterbasically used to mean a coding tree unit but may be interpreted to haveanother meaning as appropriate. The coding tree unit is typically, forexample, a 16×16 pixel block shown in FIG. 6B but may be a 32×32 pixelblock shown in FIG. 6C, a 64×64 pixel block shown in FIG. 6D, or an 8×8pixel block or a 4×4 pixel block not shown in the drawings. The codingtree unit need not necessarily be square. A coding target block orcoding tree unit in the input image 118 is hereinafter sometimesreferred to as a “prediction target block”. Furthermore, the coding unitis not limited to the pixel block such as the coding tree unit but maybe a frame, a field, or a combination thereof.

The image encoding apparatus in FIG. 1 carries out intra-prediction(also referred to as intra-frame, intra-frame prediction, or the like)or inter-prediction (also referred to as inter-picture prediction,inter-frame prediction, or the like) to generate a predicted image 127.The image encoding apparatus orthogonally transforms and quantizes aprediction error 119 between the pixel block (input image 118) and thepredicted image 127. The image encoding apparatus then carries outentropy encoding on the transformed and quantized prediction error togenerate and output encoded data 130.

The image encoding apparatus in FIG. 1 carries out encoding by selectiveapplication of a plurality of prediction modes involving different blocksizes and different methods for generating the predicted image 127. Themethod for generating the predicted image 127 is roughly classified intotwo types: intra-prediction which carries out prediction within thecoding target frame and inter-prediction which carries out predictionusing one or more reference frames temporally different from oneanother. In the present embodiment, orthogonal transformation andinverse orthogonal transformation carried out to generate a predictedimage using intra-prediction will be described in detail.

Components of the image encoding apparatus in FIG. 1 will be describedbelow.

The subtractor 101 subtracts the corresponding predicted image 127 fromthe coding target block in the input image 118 to obtain the predictionerror 119. The subtractor 101 inputs the prediction error 119 to theorthogonal transformation unit 102.

The orthogonal transformation unit 102 orthogonally transforms theprediction error 119 from the subtractor 101 to obtain transformcoefficients 120. The orthogonal transformation unit 102 will bedescribed below in detail. The orthogonal transformation unit 102 inputsthe transform coefficients 120 to the quantization unit 103.

The quantization unit 103 quantizes the transform coefficients from theorthogonal transformation unit 102 to obtain quantized transformcoefficients 121. Specifically, the quantization unit 103 carries outquantization in accordance with quantization information such as aquantization parameter and a quantization matrix which is specified bythe encoding control unit 116. The quantization parameter is indicativeof the resolution of the quantization. The quantization matrix is usedto weight the resolution of the quantization for each component of thetransform coefficients. The quantization unit 103 inputs the quantizedtransform coefficients 121 to the coefficient order control unit 113 andthe de-quantization unit 104.

The coefficient order control unit 113 transforms the quantizedtransform coefficients 121 which are a two-dimensional (2D) expressioninto a quantized transform coefficient sequence 117 which is aone-dimensional (1D) expression. The coefficient order control unit 113then inputs the quantized transform coefficient sequence 117 to theentropy encoding unit 114. The coefficient control unit 113 will bedescribed below in detail.

The entropy encoding unit 114 carries out entropy encoding (for example,Huffman encoding or arithmetic encoding) on various coding parameterssuch as the quantized transform coefficient sequence 117 from thecoefficient control unit 113, the prediction information 126 from theprediction selection unit 110, and the quantization information whichare specified by the encoding control unit 116. The coding parametersare required for decoding and include the prediction information 126,information on the transform coefficients, and information on thequantization. The coding parameters are held in an internal memory (notshown in the drawings) in the encoding control unit 116. When aprediction target block is encoded, the coding parameters for thealready coded adjacent pixel block can be used. For example, H.264intra-prediction enables a predicted value for the prediction mode ofthe prediction target block to be derived from the prediction modeinformation on the coded adjacent block.

The encoded data generated by the entropy encoding unit 114 is, forexample, multiplexed and then temporarily accumulated in the outputbuffer 115. The data is then output as the encoded data 130 inaccordance with an appropriate output timing managed by the encodingcontrol unit 116. The encoded data 130 is output to, for example, anaccumulation system (accumulation medium) or a transmission system(communication line) which is not shown in the drawings.

The de-quantization unit 104 de-quantizes the quantized transformcoefficients 121 from the quantization unit 103 to obtain a restoredtransform coefficients 122. Specifically, the de-quantization unit 104carries out de-quantization in accordance with the quantizationinformation used in the quantization unit 103. The quantizationinformation used in the quantization unit 103 is loaded from theinternal memory in the encoding control unit 116. The de-quantizationunit 104 inputs the restored transform coefficients 122 to the inverseorthogonal transformation unit 105.

The inverse orthogonal transformation unit 105 carries out an inverseorthogonal transformation corresponding to the orthogonal transformationperformed by the orthogonal transformation unit 102 on the restoredtransform coefficients 122 from the de-quantization unit 104 to obtain arestored prediction error 123. The inverse orthogonal transformationunit 105 will be described below in detail. The inverse orthogonaltransformation unit 105 inputs the restored prediction error 123 to theaddition unit 106.

The addition unit 106 adds the restored prediction error 123 and thecorresponding predicted image 127 together to generate a local decodedimage 124. The local decoded image 124 is saved to the reference imagememory 107. The local decoded image 124 saved to the reference imagememory 107 is referenced by the intra-prediction unit 108 and theinter-prediction unit 109 as a reference image 125 as necessary.

The intra-prediction unit 108 carries out intra-prediction utilizing thereference image 125 saved to the reference image memory 107. Forexample, H.264 utilizes the coded reference pixel value for the blockadjacent to the prediction target bock to compensate for pixels (copy orinterpolate pixels) along a prediction direction such as the verticaldirection or the horizontal direction to generate an intra-predictedimage. FIG. 7A shows prediction directions for the intra-predictionaccording to H.264. Furthermore, FIG. 7B shows the arrangement relationbetween reference pixels and coding target pixels according to H.264.FIG. 7C shows a method for generating a predicted image in a mode 1(horizontal prediction). FIG. 7D shows a method for generating apredicted image in a mode 4 (diagonal down-right prediction;Intra_N×N_Diagonal_Down_Right in FIG. 4A).

The intra-prediction unit 108 may interpolate pixel values using apredetermined interpolation method and then copy the interpolated pixelvalues in a predetermined prediction direction. The predictiondirections for the intra-prediction according to H.264 are illustrated,but any number of prediction modes such as 17 or 33 types of predictionmodes are made available by specifying a more detailed classification ofprediction directions. For example, H.264 defines prediction angles atintervals of 22.5 degrees, but 17 types of prediction modes including DCprediction are made available by specifying prediction angles atintervals of 11.25 degrees. Furthermore, 33 types of prediction modesincluding DC prediction are made available by specifying predictionangles at intervals of 5.625 degrees. Alternatively, instead of beingarranged at equal intervals, the angles of the prediction directions mayeach be expressed by a straight line which joins a first reference pointto a second reference point obtained by moving the first reference pointin the horizontal direction and in the vertical direction. As describedabove, the number of prediction modes can be easily increased, and thepresent embodiment is applicable regardless of the number of predictionmodes.

The inter-prediction unit 109 carries out inter-prediction utilizing thereference image 125 saved to the reference image memory 107.Specifically, the inter-prediction unit 109 carries out a block matchingprocess between the prediction target block and the reference image 125to derive the amount of deviation in motion (motion vector). Theinter-prediction unit 109 carries out an interpolation process (motioncompensation) based on the motion vector to generate an inter-predictedimage. H.264 enables the interpolation process to be achieved to anaccuracy of a ¼ pixel. The derived motion vector is subjected to entropyencoding as a part of the prediction information 126.

The selection switch 111 selects an output end of the intra-predictionunit 108 or an output end of the inter-prediction unit 109 in accordancewith the prediction information 126 from the prediction selection unit110. The selection switch 111 then inputs an intra-predicted image or aninter-predicted image to the subtraction unit 101 and the addition unit106 as the predicted image 127. If the prediction information 126 isindicative of intra-prediction, the selection switch 110 acquires theintra-predicted image from the intra-prediction unit 108 as a predictedimage 127. On the other hand, if the prediction information 126 isindicative of inter-prediction, the selection switch 110 acquires theinter-predicted image from the inter-prediction unit 109 as a predictedimage 127.

The prediction selection unit 110 has a function to set the predictioninformation 126 in accordance with the prediction mode controlled by theencoding control unit 116. As described above, the intra-prediction orthe inter-prediction can be selected for generation of the predictedimage 127. Moreover, a plurality of modes can further be selected foreach of the intra-prediction or the inter-prediction. The encodingcontrol unit 116 determines one of the plurality of prediction modes forthe intra-prediction and the inter-prediction to be the optimumprediction mode. The prediction selection unit 110 sets the predictioninformation 126 according to the determined optimum prediction mode.

For example, in connection with the intra-prediction, the predictionmode information from the encoding control unit 116 is specified in theintra-prediction unit 108. In accordance with the prediction modeinformation, the intra-prediction unit 108 generates the predicted image127. The encoding control unit 116 may specify a plurality of pieces ofprediction mode information in order of increasing number of theprediction mode or decreasing number of the prediction mode.Furthermore, the encoding control unit 116 may limit the prediction modein accordance with the characteristics of the input image. The encodingcontrol unit 116 need not specify all the prediction modes but mayspecify at least one piece of prediction mode information for the codingtarget block.

For example, the encoding control unit 116 determines the optimumprediction mode using a cost function shown in:

K=SAD+λ×OH  (1)

In Expression (1), OH denotes the amount of code for the predictioninformation 126 (for example, motion vector information and predictionblock size information), and SAD denotes the sum of absolute differencebetween the prediction target block and the predicted image 127 (thatis, the accumulated sum of the absolute values of the prediction error119). Furthermore, λ denotes a Lagrange multiplier determined based onthe value of the quantization information (quantization parameter), andK denotes a coding cost. If Expression (1) is used, the prediction modewhich minimizes the coding cost K is determined to be optimum in termsof the amount of generated code and prediction errors. As a modificationof Expression (1), the coding cost may be evaluated only from the OH orthe SAD or by utilizing a value obtained by carrying out an Hadamardtransformation on the SAD or a value approximate thereto.

Furthermore, the optimum prediction mode can be determined using aprovisionally encoding unit (not shown in the drawings). For example,the encoding control unit 116 determines the optimum prediction modeusing a cost function shown in:

J=D+λ×R  (2)

In Expression (2), D denotes the sum of square differences (that is,coding distortion) between the prediction target block and a localdecoded image, R denotes the amount of code estimated by provisionallyencoding the predicted error between the prediction target block and thepredicted image 127 for the prediction mode, and J denotes the codingcost. To derive the coding cost in Expression (2), a provisionallyencoding process and a local decoding process need to be carried out ineach prediction mode. This increases the scale of relevant circuits orthe amount of calculation. On the other hand, the coding cost J isderived based on a more accurate coding distortion and a more accurateamount of code. Therefore, the optimum prediction mode is accuratelydetermined to allow a high coding efficiency to be easily maintained. Asa modification of Expression (2), the coding cost may be evaluated onlyfrom the R or the D or by utilizing a value approximate to the R or theD. Furthermore, the encoding control unit 116 may, in advance, narrowdown the number of candidates for the prediction mode one of which isdetermined using Expression (1) or Expression (2), based on informationpre-obtained for the prediction target block (prediction modes for thesurrounding pixel blocks, the results of image analysis, and the like).

The encoding control unit 116 controls the components of the imageencoding apparatus in FIG. 1. Specifically, the encoding control unit116 performs various control operations for an encoding processincluding the above-described operations.

The 1D transform matrix set unit 112 generates 1D transform matrix setinformation 129 based on the prediction mode information included in theprediction information 126 from the prediction selection unit 110. The1D transform matrix set unit 112 then inputs the 1D transform matrix setinformation 129 to the orthogonal transformation unit 102 and theinverse orthogonal transformation unit 105. The 1D transform matrix setinformation 129 will be described below in detail.

The orthogonal transformation unit 102 according to the presentembodiment will be described below in detail with reference to FIG. 2.

The orthogonal transformation unit 102 includes a selection switch 201,a vertical transformation unit 202, a transposition unit 203, aselection switch 204, and a horizontal transformation unit 205. Thevertical transformation unit 202 includes a 1D orthogonal transformationunit A 206 and a 1D orthogonal transformation unit B 207. The horizontaltransformation unit 205 includes a 1D orthogonal transformation unit A208 and a 1D orthogonal transformation unit B 209. The order of thevertical transformation unit 202 and the horizontal transformation unit205 is illustrative and may be reversed.

The 1D orthogonal transformation unit A 206 and the 1D orthogonaltransformation unit A 208 have common functions in that both unitsmultiply an input matrix by a 1D transform matrix A. The 1D orthogonaltransformation unit B 207 and the 1D orthogonal transformation unit B209 have common functions in that both units multiply the input matrixby a 1D transform matrix B. Thus, the 1D orthogonal transformation unitA 206 and the 1D orthogonal transformation unit A 208 can also beimplemented by using physically the same hardware in a time divisionmanner. This also applies to the 1D orthogonal transformation unit B 207and the 1D orthogonal transformation unit B 209.

The selection switch 201 leads the prediction error 119 to one of the 1Dorthogonal transformation unit A 206 and the 1D orthogonaltransformation unit B 207 in accordance with a vertical transform indexincluded in the 1D transform matrix set information 129. The 1Dorthogonal transformation unit A 206 multiplies the input predictionerror (matrix) 119 by a 1D transform matrix A and outputs the product.The 1D orthogonal transformation unit B 207 multiplies the inputprediction error 119 by a 1D transform matrix B and outputs the product.Specifically, the 1D orthogonal transformation unit A 206 and the 1Dorthogonal transformation unit B 207 (that is, the verticaltransformation unit 202) carries out a one-dimensional orthogonaltransformation shown in Expression (3) to eliminate a verticalcorrelation in the prediction error 119.

Y=VX  (3)

In Expression (3), X denotes a matrix (N×N) of the prediction error 119,V comprehensively denotes the 1D transform matrix A and the 1D transformmatrix B (both are N×N matrices), and Y denotes an output matrix (N×N)from each of the 1D orthogonal transformation unit A 206 and the 1Dorthogonal transformation unit B 207. Specifically, the transform matrixV is an N×N transform matrix in which a transform basis designed toeliminate the vertical correlation in the matrix X is vertically as rowvectors. However, as described below, the 1D transform matrix A and the1D transform matrix B are designed in different manners and havedifferent types of nature. The 1D transform matrix A and the 1Dtransform matrix B may use integers obtained by the designed transformbasis subjected to scalar multiplication.

Here, if the prediction error 119 is a rectangular block expressed asM×N, the size of the block to be orthogonally transformed may also beM×N.

The transposition unit 203 transposes the output matrix (Y) from thevertical transformation unit 202 and provides the transposed outputmatrix (Y) to the selection switch 204. However, the transposition unit203 is illustrative, and the corresponding hardware need not necessarilybe prepared. For example, the output matrix (Y) can be transposedwithout the need to prepare the hardware corresponding to thetransposition unit 203 by saving the results of a 1D orthogonaltransformation carried out by the vertical transformation unit 202 (eachof the elements of the output matrix from the vertical transformationunit 202) and loading the results in an appropriate order when thehorizontal transformation unit 205 performs a 1D orthogonaltransformation.

The selection switch 204 leads the input matrix from the transpositionunit 203 to one of the 1D orthogonal transformation unit A 208 and the1D orthogonal transformation unit B 209 in accordance with a horizontaltransform index included in the 1D transform matrix set information 129.The 1D orthogonal transformation unit A 208 multiplies the input matrixby the 1D transform matrix A and outputs the product. The 1D orthogonaltransformation unit B 209 multiplies the input matrix by the 1Dtransform matrix B and outputs the product. Specifically, the 10orthogonal transformation unit A 208 and the 1D orthogonaltransformation unit B 209 (that is, the horizontal transformation unit205) carries out a one-dimensional orthogonal transformation shown inExpression (4) to eliminate a horizontal correlation in the predictionerror.

Z=HY ^(T)  (4)

In Expression (4), H comprehensively denotes the 1D transform matrix Aand the 1D transform matrix B (both are N×N matrices), and Z denotes anoutput matrix (N×N) from each of the 1D orthogonal transformation unit A208 and the 1D orthogonal transformation unit B 209; the output matrixis indicative of the transform coefficients 120. Specifically, thetransform matrix H is an N×N transform matrix in which a transform basisdesigned to eliminate the horizontal correlation in the matrix Y isvertically arranged as row vectors. As described above, the 1D transformmatrix A and the 1D transform matrix B are designed in different mannersand have different types of nature. Furthermore, the 1D transform matrixA and the 1D transform matrix B may use integers obtained by thedesigned transform basis subjected to scalar multiplication.

As described above, the orthogonal transformation unit 102 carries outan orthogonal transformation in accordance with the 1D transform matrixset information 129 input from the 1D transform matrix set unit 112, onthe prediction error (matrix) 119 to generate the transform coefficients(matrix) 120. With H.264 taken into account, the orthogonaltransformation unit 102 may include a DCT unit (not shown in thedrawings) or one of the 1D transform matrix A and the 1D transformmatrix B may be replaced with a matrix for DCT. For example, the 1Dtransform matrix B may be a transform matrix for DCT. Moreover, theorthogonal transformation unit 102 may implement, in addition to DCT,various orthogonal transformations such as a Hadamard transformation,Karhunen Loeve transformation described below, and discrete sinetransformation.

Now, the difference in nature between the 1D transform matrix A and the1D transform matrix B will be described. Some intra-prediction modessupported by H.264 and the like generate a predicted image by copying,along a prediction direction, a group of reference pixels on one or bothof adjacent lines located to the left of and above the prediction targetblock or carrying out similar copying after interpolation. That is, thisintra-prediction mode selects at least one reference pixel from thegroup of reference pixels in accordance with the prediction directionand copies the reference pixel or carries out interpolation using thereference pixels, to generate a predicted image. The intra-predictionmode utilizes the spatial correlation in an image and thus has aprediction accuracy which tends to decrease with increasing distancefrom the reference pixel. That is, the absolute value of the predictionerror is likely to increase consistently with the distance from thereference pixel. The tendency is similarly exhibited regardless of theprediction direction. More specifically, in connection with theintra-prediction modes (for example, the mode 1 and mode 8 in FIG. 7A)in which only the group of reference pixels on the line located to theleft of and adjacent to the prediction target block is referenced (thepixel values of the reference pixels are copied or interpolation iscarried out using the reference pixels), the prediction error exhibitsthe tendency in the horizontal direction. In connection with theprediction modes in which only the group of reference pixels on the linelocated above and adjacent to the prediction target block is referenced(for example, the mode 0, mode 3, and mode 7 in FIG. 7A), the predictionerror exhibits the tendency in the vertical direction. Moreover, inconnection with the prediction modes (for example, the mode 4, mode 5,and mode 6 in FIG. 7A) in which the groups of reference pixels on theline located to the left of and adjacent to the prediction target blockand on the line located above and adjacent to the prediction targetblock are referenced, the prediction error exhibits such a tendency inthe horizontal direction and vertical direction. In general, thetendency is exhibited in the direction orthogonal to the line of thegroup of reference pixels utilized to generate a predicted image.

The 1D transform matrix A is generated by pre-designing a commontransform basis so as to increase, compared to the 1D transform matrixB, a coefficient density after 1D orthogonal transformation (that is, toreduce the rate of nonzero coefficients in the quantized transformcoefficients 121) in the orthogonal direction (vertical direction orhorizontal direction). On the other hand, the 1D transform matrix B isgenerated by designing a general-purpose transform matrix having no suchnature. For example, the general-purpose transformation is DCT. Theefficiency of transformation of the prediction error in theintra-prediction and thus the coding efficiency are improved by carryingout a 1D orthogonal transformation in the orthogonal direction using the1D transform matrix A. For example, the prediction error 119 in the mode0 (vertical prediction) exhibits the tendency in the vertical directionbut not in the horizontal direction. Hence, efficient orthogonaltransformation can be achieved by carrying out a 1D orthogonaltransformation in the vertical transformation unit 202 using the 1Dtransform matrix A and carrying out a 1D orthogonal transformation inthe horizontal transformation unit 205 using the 1D transform matrix B.

The inverse orthogonal transformation unit 105 according to the presentembodiment will be described below in detail with reference to FIG. 3.

The inverse orthogonal transformation unit 105 includes a selectionswitch 301, a vertical inverse transformation unit 302, a transpositionunit 303, a selection switch 304, and a horizontal inversetransformation unit 305. The vertical inverse transformation unit 302includes a 1D inverse orthogonal transformation unit A 306 and a 1Dinverse orthogonal transformation unit B 307. The horizontal inversetransformation unit 305 includes a 1D inverse orthogonal transformationunit A 308 and a 1D inverse orthogonal transformation unit B 309. Theorder of the vertical inverse transformation unit 302 and the horizontalinverse transformation unit 305 is illustrative and may be reversed.

The 1D inverse orthogonal transformation unit A 306 and the 1D inverseorthogonal transformation unit A 308 have common functions in that bothunits multiply an input matrix by a transposed matrix of the 1Dtransform matrix A. The 1D inverse orthogonal transformation unit B 307and the 1D inverse orthogonal transformation unit B 309 have commonfunctions in that both units multiply an input matrix by a transposedmatrix of the 1D transform matrix B. Thus, the 1D inverse orthogonaltransformation unit A 306 and the 1D inverse orthogonal transformationunit A 308 can also be implemented by using physically the same hardwarein a time division manner. This also applies to the 1D inverseorthogonal transformation unit B 307 and the 1D inverse orthogonaltransformation unit B 309.

The selection switch 301 leads the restored transform coefficients 122to one of the 1D inverse orthogonal transformation unit A 306 and the 1Dinverse orthogonal transformation unit B 307 in accordance with thevertical transform index included in the 1D transform matrix setinformation 129. The 1D inverse orthogonal transformation unit A 306multiplies the input restored transform coefficients 122 (matrix form)by a transposed matrix of the 1D transform matrix A and outputs theproduct. The 1D inverse orthogonal transformation unit B 307 multipliesthe input restored transform coefficients 122 by a transposed matrix ofthe 1D transform matrix B and outputs the product. Specifically, the 1Dinverse orthogonal transformation unit A 306 and the 1D inverseorthogonal transformation unit B 307 (that is, the vertical inversetransformation unit 302) carry out a one-dimensional inverse orthogonaltransformation shown in:

Y′=V ^(T) Z′  (5)

In Expression (5), Z′ denotes a matrix (N×N) of the restored transformcoefficients 122, V^(T) comprehensively denotes the transposed matricesof the 1D transform matrix A and the 1D transform matrix B (both are N×Nmatrices), and Y′ denotes an output matrix (N×N) from each of the 1Dinverse orthogonal transformation unit A 306 and the 1D inverseorthogonal transformation unit B 307.

The transposition unit 303 transposes the output matrix (Y′) from thevertical inverse transformation unit 302 and outputs the transposedoutput matrix to the selection switch 304. However, the transpositionunit 303 is illustrative, and the corresponding hardware need notnecessarily be prepared. For example, the output matrix (Y′) can betransposed without the need to prepare the hardware corresponding to thetransposition unit 303 by saving the results of a 1D inverse orthogonaltransformation carried out by the vertical transformation unit 302 (eachof the elements of the output matrix from the vertical inversetransformation unit 302) and loading the results in an appropriate orderwhen the horizontal inverse transformation unit 305 performs a 1Dinverse orthogonal transformation.

The selection switch 304 leads the input matrix from the transpositionunit 303 to one of the 1D inverse orthogonal transformation unit A 308and the 1D inverse orthogonal transformation unit B 309 in accordancewith a horizontal transform index included in the 1D transform matrixset information 129. The 1D inverse orthogonal transformation unit A 308multiplies the input matrix by the transposed matrix of the 10 transformmatrix A and outputs the product. The 1D inverse orthogonaltransformation unit B 309 multiplies the input matrix by the transposedmatrix of the 1D transform matrix B and outputs the product.Specifically, the 10 inverse orthogonal transformation unit A 308 andthe 10 inverse orthogonal transformation unit B 309 (that is, thehorizontal inverse transformation unit 305) carry out a one-dimensionalinverse orthogonal transformation shown in:

X′=H ^(T) Y′ ^(T)  (6)

In Expression (6), HT comprehensively denotes the transposed matrices ofthe 1D transform matrix A and the 1D transform matrix B (both are N×Nmatrices), and X′ denotes an output matrix (N×N) from each of the 10inverse orthogonal transformation unit A 308 and the 1D inverseorthogonal transformation unit B 309; the output matrix is indicative ofthe restored prediction error 123.

As described above, the inverse orthogonal transformation unit 105carries out an orthogonal transformation in accordance with the 1Dtransform matrix set information 129 input from the 10 transform matrixset unit 112, on the restored transform coefficients (matrix) 122 togenerate the restored prediction error (matrix) 123. With H.264 takeninto account, the inverse orthogonal transformation unit 105 may includean IDCT unit (not shown in the drawings) or one of the 1D transformmatrix A and the 1D transform matrix B may be replaced with a matrix forDCT. For example, the 1D transform matrix B may be a transform matrixfor DCT. Moreover, the inverse orthogonal transformation unit 105 mayimplement, in addition to IDCT, inverse orthogonal transformationscorresponding to various orthogonal transformations such as an Hadamardtransformation, Karhunen Loeve transformation described below, anddiscrete sine transformation for coordination with the orthogonaltransformation unit 102.

The 1D transform matrix set information 129 according to the presentembodiment which is generated by the 1D transform matrix set unit 112will be described below in detail.

The 1D transform matrix set information 129 directly or indirectlyindicates the vertical transform index for selection of a transformmatrix for use in vertical orthogonal transformation and verticalinverse orthogonal transformation and the horizontal transform index forselection of a transform matrix for use in horizontal orthogonaltransformation and horizontal inverse orthogonal transformation. Forexample, the 1D transform matrix set information 129 can be expressed bya transform index (TrasformIdx) shown in FIG. 4D. Reference to the tablein FIG. 4D allows a vertical transform index (Vertical Transform Idx)and a horizontal transform index (Horizontal Transform Idx) to bederived from the transform index.

As shown in FIG. 4B, a vertical transform index of “0” allows selectionof the 1D transform matrix A (1D_Transform_Matrix_A) or the transposedmatrix thereof for vertical orthogonal transformation or verticalinverse orthogonal transformation. On the other hand, a verticaltransform index of “1” allows selection of the 1D transform matrix B(1D_Transform_Matrix_B) or the transposed matrix thereof for verticalorthogonal transformation or vertical inverse orthogonal transformation.

As shown in FIG. 4C, a horizontal transform index of “0” allowsselection of the 1D transform matrix A (1D_Transform_Matrix_A) or thetransposed matrix thereof for horizontal orthogonal transformation orhorizontal inverse orthogonal transformation. On the other hand, ahorizontal transform index of “1” allows selection of the 1D transformmatrix B (1D_Transform_Matrix_B) or the transposed matrix thereof forhorizontal orthogonal transformation or horizontal inverse orthogonaltransformation.

Furthermore, FIG. 4A illustrates the index for each (intra-) predictionmode (IntraN×NPredModeIndex), the name thereof (Name ofIntraN×NPredMode), and the corresponding vertical transform index andhorizontal transform index. In FIG. 4A, “N×N” is indicative of the sizeof the prediction target block (N=4, 8, 16, or the like). The size ofthe prediction target block can be expanded to “M×N” (that is,rectangles other than squares).

FIG. 4E is obtained by integrating FIG. 4A and FIG. 4D together andshows the index for each prediction mode, the name of the index, and thecorresponding transform index.

The 1D transform matrix set unit 112 detects the index of the predictionmode from the prediction mode information included in the predictioninformation 126. The 1D transform matrix set unit 112 then generates thecorresponding 1D transform matrix set information 129. The tables shownin FIG. 4A, FIG. 4B, FIG. 4C, FIG. 4D, and FIG. 4E are illustrative. The1D transform matrix set unit 112 may generate the 1D transform matrixset information 129 while avoiding the use of some or all of the tables.

For example, TransformIdx indicative of 0 means that the verticaltransform index indicates 0 and that the horizontal transform indexindicates 0. This means that the 1D transform matrix A is used forvertical orthogonal transformation and that the 1D transform matrix A isused for horizontal orthogonal transformation. These index values alsomean that the transposed matrix of the 1D transform matrix A is used forvertical inverse orthogonal transformation and that the transposedmatrix of the 1D transform matrix A is used for horizontal inverseorthogonal transformation.

TransformIdx indicative of 1 means that the vertical transform indexindicates 0 and that the horizontal transform index indicates 1. Thismeans that the 1D transform matrix A is used for vertical orthogonaltransformation and that the 1D transform matrix B is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix A is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix B is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 2 means that the vertical transform indexindicates 1 and that the horizontal transform index indicates 0. Thismeans that the 1D transform matrix B is used for vertical orthogonaltransformation and that the 1D transform matrix A is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix B is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix A is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 3 means that the vertical transform indexindicates 1 and that the horizontal transform index indicates 1. Thismeans that the 1D transform matrix B is used for vertical orthogonaltransformation and that the 1D transform matrix B is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix B is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix B is used for horizontal inverse orthogonaltransformation.

The table shown in FIG. 4A assigns the 1D transform matrix setinformation 129 taking the above-described tendency of eachintra-prediction mode into account. That is, 0 is assigned to thevertical transform index for the prediction modes exhibiting thetendency in the vertical direction of the prediction error. 0 isassigned to the horizontal transform index for the prediction modesexhibiting the tendency in the horizontal direction. On the other hand,1 is assigned to each of the directions not exhibiting the tendency.When the vertical and horizontal directions of the prediction modes areclassified into two classes depending whether or not the tendency ispresent and the 1D transform matrix A or the 1D transform matrix B isadaptively applied to each of the vertical and horizontal directions, ahigher transform efficiency can be achieved than in a case where fixedorthogonal transformation such as DCT is uniformly applied to theprediction modes.

The coefficient order control unit 113 will be described below indetail.

The coefficient order control unit 113 transforms the quantizedtransform coefficients 121, which are a two-dimensional expression, intothe quantized transform coefficient sequence 117 which is aone-dimensional expression by arranging the elements of the quantizedtransform coefficients 121 according to a predetermined order. By way ofexample, the coefficient order control unit 113 can carry out a common2D-1D transformation regardless of the prediction mode. Specifically,the coefficient order control unit 113 can utilize a zigzag scan as isthe case with H.264. The zigzag scan arranges the elements of thequantized transform coefficients 121 in such an order as shown in FIG.8A and transforms the elements into such a quantized transformcoefficient sequence 117 as shown in FIG. 8B. In FIG. 8A and FIG. 8B,(i, j) denotes the coordinates (position information) of each element inthe quantized transform coefficients (matrix) 121. Furthermore, FIG. 8Cshows a 2D-1D transformation utilizing the zigzag scan (in the case of a4×4 pixel block). Specifically, FIG. 8C shows an index (idx) indicativeof the order of coefficients (the order of scans) in the quantizedtransform coefficient sequence 117 subjected to the 2D-1D transformationutilizing the zigzag scan, and the corresponding elements (cij) of thequantized transform coefficients 121. In FIG. 8C, cij denotes theelements with the coordinates (i, j) in the quantized transformcoefficients (matrix) 121.

In another example, the coefficient order control unit 113 can carry outindividual 2D-1D transformations for the respective prediction modes.The coefficient order control unit 113 performing such an operation isillustrated in FIG. 5A. The coefficient order control unit 113 includesa selection switch 501 and individual 2D-1D transformation units 502, .. . , and 510 for the respective nine types of prediction modes. Inaccordance with the prediction mode information (for example, theindices of the prediction modes in FIG. 4A) included in the predictioninformation 126, the selection switch 501 leads the quantized transformcoefficients 121 to the 2D-1D transformation unit corresponding to theprediction mode (one of the 2D-1D transformation units 502, . . . ,510). For example, a prediction mode index of 0 allows the selectionswitch 501 to lead the quantized transform coefficients 121 to the 2D-1Dtransformation unit 502. In FIG. 5A, the prediction modes and the 2D-1Dtransformation units are in a one-to-one correspondence. The quantizedtransform coefficients 121 are led to one 2D-1D transformation unitcorresponding to the prediction mode. FIG. 9 illustrates the 2D-1Dtransformation carried out by each of the 2D-1D transformation units502, . . . , 510 (in the case of a 4×4 pixel block). A specific designtechnique for the 2D-1D transformation for each prediction mode as shownin FIG. 9 will be described below. FIG. 9 shows the index (idx)indicative of the order of coefficients (the order of scans) in thequantized transform coefficient sequence 117 subjected to the 2D-1Dtransformation by the 2D-1D transformation unit corresponding to eachprediction mode, and the corresponding elements (cij) of the quantizedtransform coefficients 121. In FIG. 9, cij denotes the elements with thecoordinates (i, j) in the quantized transform coefficients (matrix) 121.Furthermore, in FIG. 9, each prediction mode is expressed by its name,and the correspondence between the names and the prediction mode indexis as shown in FIG. 4A. Thus, the application of the individual 2D-1Dtransformations for the respective prediction modes, for example, allowsthe coefficients to be scanned in an order suitable for the tendency togenerate nonzero coefficients in the quantized transform coefficients121 for each prediction mode. This improves the coding efficiency.

For simplification, the example regarding the 4×4 pixel block is shown.However, for an 8×8 pixel block, a 16×16 pixel block, and the like, theindividual 2D-1D transformations for the respective prediction modes cansimilarly be defined. Furthermore, if the pixel block is a rectangularblock expressed as M×N, the size of the block to be subjected to 2D-1Dtransformation may also be M×N. In this case, for the rectangular block,such individual 2D-1D transformations as illustrated in FIG. 9 may bedefined for the respective prediction modes.

In yet another example, the coefficient order control unit 113 maydynamically update the scan order for the 2D-1D transformation. Thecoefficient order control unit 113 performing such an operation isillustrated in FIG. 5B. The coefficient order control unit 113 includesthe selection switch 501, the individual 2D-1D transformation units 502,. . . , and 510 for the respective nine types of prediction modes, anoccurrence frequency count unit 511, and a coefficient order update unit512. The selection switch 501 is as described with reference to FIG. 5A.The individual 2D-1D transformation units 502, . . . , and 510 for therespective nine types of prediction modes are different from the 2D-1Dtransformation units shown in FIG. 5A in that the scan order for the2D-1D transformation units 502, . . . , and 510 is updated by thecoefficient order update unit 512.

The occurrence frequency count unit 511 creates, for each predictionmode, a histogram of the number of occurrences of nonzero coefficientsin each element of the quantized transform coefficient sequence 117. Theoccurrence frequency count unit 511 inputs the created histogram 513 tothe coefficient order update unit 512.

The coefficient order update unit 512 updates the order of coefficientsat a predetermined timing based on the histogram 513. The timing may be,for example, a timing when an encoding process carried out on a codingtree unit is finished or a timing when an encoding process carried outon one line in the coding tree unit is finished.

Specifically, the coefficient order update unit 512 references thehistogram 513 to update the order of coefficients for a prediction modewith an element for which the counted number of occurrences of nonzerocoefficients is equal to or larger than a threshold. For example, thecoefficient order update unit 512 performs the updating for a predictionmode with an element for which the counted number of occurrences ofnonzero coefficients is 16 or more. Setting a threshold for the numberof occurrences allows the order of coefficients to be globally updated,thus avoiding convergence to a local optimum solution.

The coefficient order update unit 512 sorts, for the updating-targetprediction mode, the elements in order of decreasing occurrencefrequency of nonzero coefficients. The sorting can be achieved inaccordance with an existing algorithm, for example, bubble sort or quicksort. The coefficient order update unit 512 inputs coefficient orderupdate information 514 indicative of the sorted order of the elements tothe 2D-1D transformation unit corresponding to the updating-targetprediction mode.

Once the coefficient order update information 514 is input to the 2D-1Dtransformation unit, the 2D-1D transformation unit carries out a 2D-1Dtransformation in accordance with the updated scan order. If the scanorder is dynamically updated, initial scan orders for the 2D-1Dtransformation units need to be set. For example, the zigzag scan or thescan order illustrated in FIG. 9 can be utilized as the initial scanorder.

The dynamic updating of the scan order is expected to achieve a stablyhigh coding efficiency even if the tendency to generate nonzerocoefficients in the quantized transform coefficients 121 variesdepending on the nature of the predicted image, the quantizationinformation (quantization parameter), and the like. Specifically, theamount of code generated in run length coding in the entropy encodingunit 114 can be reduced.

For simplification, H.264 has been illustrated and the case of the ninetypes of prediction modes has been described. However, even if thenumber of types of the prediction mode is increased to 17, 33, or thelike, the individual 2D-1D transformations for the respective predictionmodes can be achieved by adding 2D-1D transformation units correspondingto the prediction modes resulting from the increase.

Processing carried out on the coding target block (coding tree unit) bythe image encoding apparatus in FIG. 1 will be described below withreference to FIG. 10A and FIG. 10B. In the example shown in FIG. 10A andFIG. 10B, it is assumed that the orthogonal transformation and inverseorthogonal transformation according to the present embodiment (that is,the adaptive orthogonal transformation and inverse orthogonaltransformation based on the 1D transform matrix set information 129) areenable. However, as described below, the syntax may be specified to makethe orthogonal transformation and inverse orthogonal transformationaccording to the present embodiment disable.

Once the input image 118 is input to the image encoding apparatus inFIG. 1 in units of coding target block, a process of encoding the codingtarget block is started (step S601). The intra-prediction unit 108 andthe inter-prediction unit 109 uses the reference image 125 saved to thereference image memory 107 to generate an intra-predicted image and aninter-predicted image (step S602). The encoding control unit 116determines the optimum prediction mode in terms of the above-describedcoding cost to generate the prediction information 126 (step S603). Theprediction information 126 is input to each element by the predictionselection unit 110 as described above. If the prediction information 126generated in step S603 is indicative of intra-prediction, the processingproceeds to step S605. If the prediction information 126 generated instep S603 is indicative of inter-prediction, the processing proceeds tostep S605′.

In step S605, the subtraction unit 101 subtracts the (intra-) predictedimage 127 from the coding target block to generate the prediction error119. The processing then proceeds to step S606. On the other hand, alsoin step S605′, the subtraction unit 101 subtracts the (inter-) predictedimage 127 from the coding target block to generate the prediction error119. The processing then proceeds to step S614′.

In step S606, the 1D transform matrix set unit 112 extracts theprediction mode information included in the prediction information 126generated in step S603. Based on the extracted prediction modeinformation (for example, with reference to the table in FIG. 4A), the1D transform matrix set unit 112 generates the 1D transform matrix setinformation 129 (step S607). The 1D transform matrix set unit 112 inputsthe 1D transform matrix set information 129 to the orthogonaltransformation unit 102 and the inverse orthogonal transformation unit105.

The selection switch 201 in the orthogonal transformation unit 102selects the 1D orthogonal transformation unit A 206 or the 1D orthogonaltransformation unit B 207 based on the 1D transform matrix setinformation 129 (step S608, step S609, and step S610). On the otherhand, the selection switch 204 in the orthogonal transformation unit 102selects the 1D orthogonal transformation unit A 208 or the 1D orthogonaltransformation unit B 209 based on the 1D transform matrix setinformation 129 (step S611, step S612, and step S613). The processingthen proceeds to step S614.

For example, if the transform index (TransformIdx), an example of the 1Dtransform matrix set information 129, is 0, the selection switch 201selects the 1D orthogonal transformation unit A 206 in the verticaltransformation unit 202 (step S609). If TransformIdx is 0, the selectionswitch 204 selects the 1D orthogonal transformation unit A 208 in thehorizontal transformation unit 205 (step S612). If TransformIdx is 1,the selection switch 201 selects the 1D orthogonal transformation unit A206 in the vertical transformation unit 202 (step S609). If TransformIdxis 1, the selection switch 204 selects the 1D orthogonal transformationunit B 209 in the horizontal transformation unit 205 (step S613). IfTransformIdx is 2, the selection switch 201 selects the 1D orthogonaltransformation unit B 207 in the vertical transformation unit 202 (stepS610). If TransformIdx is 2, the selection switch 204 selects the 1Dorthogonal transformation unit A 208 in the horizontal transformationunit 205 (step S612). If TransformIdx is 3, the selection switch 201selects the 1D orthogonal transformation unit B 207 in the verticaltransformation unit 202 (step S610). If TransformIdx is 3, the selectionswitch 204 selects the 1D orthogonal transformation unit B 209 in thehorizontal transformation unit 205 (step S613).

In step S614, the orthogonal transformation unit 102 carries out avertical transformation and a horizontal transformation which correspondto the settings made in step S608, . . . , and step S613, on theprediction error 119 to generate the transform coefficients 120.Subsequently, the quantization unit 103 quantizes the transformcoefficients 120 generated in step S614 (step S615). The processing thenproceeds to step S616.

On the other hand, in step S614′, the orthogonal transformation unit 102carries out fixed orthogonal transformation, for example, DCT, on theprediction error 119 to generate the transform coefficients 120.Subsequently, the quantization unit 103 quantizes the transformcoefficients 120 generated in step S614′ to generate the quantizedtransform coefficients 121 (step S615′). The processing proceeds to stepS617′. The orthogonal transformation carried out in step S614′ may beimplemented by the DCT unit (not shown in the drawings) or by the 1Dorthogonal transformation unit B 207 and the 1D orthogonaltransformation unit B 209.

In step S616, the coefficient order control unit 113 sets the scan order(that is, in the example shown in FIG. 5A and FIG. 5B, the unit to whichthe selection switch 501 is connected) based on the prediction modeinformation included in the prediction information 126 generated in stepS603. The processing proceeds to step S617. If the coefficient ordercontrol unit 113 carries out a common 2D-1D transformation regardless ofthe prediction mode, step S616 may be omitted.

In step S617, the coefficient order control unit 113 carries out a 2D-1Dtransformation corresponding to the setting made in step S616, on thequantized transform coefficients 121 to generate the quantized transformcoefficient sequence 117. Subsequently, the entropy encoding unit 114carries out entropy encoding on the coding parameters including thequantized transform coefficient sequence 117 (step S618). The encodeddata 130 is output at the appropriate timing managed by the encodingcontrol unit 116. On the other hand, the de-quantization unit 104de-quantizes the quantized transform coefficients 121 to generate therestored transform coefficients 122 (step S619). The processing proceedsto step S620.

In step S617′, the coefficient order control unit 113 carries out, forexample, fixed 2D-1D transformation such as the zigzag scan or 2D-1Dtransformation corresponding to Intra_N×N_DC in FIG. 9, on the quantizedtransform coefficient sequence 121 to generate the quantized transformcoefficient sequence 117. Subsequently, the entropy encoding unit 114carries out entropy encoding on the coding parameters including thequantized transform coefficient sequence 117 (step S618′). The encodeddata 130 is output at the appropriate timing managed by the encodingcontrol unit 116. On the other hand, the de-quantization unit 104de-quantizes the quantized transform coefficients 121 to generate therestored transform coefficients 122 (step S619′). The processing thenproceeds to step S626′.

The selection switch 301 in the inverse orthogonal transformation unit105 selects the 1D inverse orthogonal transformation unit A 306 or the1D inverse orthogonal transformation unit B 307 based on the 1Dtransform matrix set information 129 (step S620, step S621, and stepS622). On the other hand, the selection switch 304 in the inverseorthogonal transformation unit 105 selects the 1D inverse orthogonaltransformation unit A 308 or the 1D inverse orthogonal transformationunit B 309 based on the 1D transform matrix set information 129 (stepS623, step S624, and step S625). The processing then proceeds to stepS626.

For example, if the transform index (TransformIdx), an example of the 1Dtransform matrix set information 129, is 0, the selection switch 301selects the 1D inverse orthogonal transformation unit A 306 in thevertical inverse transformation unit 302 (step S621). If TransformIdx is0, the selection switch 304 selects the 1D inverse orthogonaltransformation unit A 308 in the horizontal inverse transformation unit305 (step S624). If TransformIdx is 1, the selection switch 301 selectsthe 1D inverse orthogonal transformation unit A 306 in the verticalinverse transformation unit 302 (step S621). If TransformIdx is 1, theselection switch 304 selects the 1D inverse orthogonal transformationunit B 309 in the horizontal inverse transformation unit 305 (stepS625). If TransformIdx is 2, the selection switch 301 selects the 1Dinverse orthogonal transformation unit B 307 in the vertical inversetransformation unit 302 (step S622). If TransformIdx is 2, the selectionswitch 304 selects the 1D inverse orthogonal transformation unit A 308in the horizontal inverse transformation unit 305 (step S624). IfTransformIdx is 3, the selection switch 301 selects the 1D inverseorthogonal transformation unit B 307 in the vertical inversetransformation unit 302 (step S622). If TransformIdx is 3, the selectionswitch 304 selects the 1D inverse orthogonal transformation unit B 309in the horizontal inverse transformation unit 305 (step S625).

In step S626, the inverse orthogonal transformation unit 105 carries outa vertical transformation and a horizontal transformation whichcorrespond to the settings made in step S620, . . . , and step S625, onthe restored transform coefficients 122 to generate the restoredprediction error 123. The processing proceeds to step S627. In stepS626′, the inverse orthogonal transformation unit 105 carries out aninverse orthogonal transformation, for example, IDCT, on the restoredtransform coefficients 123 to generate the restored prediction error123. The processing then proceeds to step S627. The fixed inverseorthogonal transformation carried out in step S626′ may be implementedby the IDCT unit (not shown in the drawings) or by the 1D inverseorthogonal transformation unit B 307 and the 1D inverse orthogonaltransformation unit B 309.

In step S627, the addition unit 106 adds the restored prediction error123 generated in step S626 or step S626′ to the predicted image 127 togenerate the local decoded image 124. The local decoded image 124 issaved to the reference image memory 107 as a reference image. Thus, theprocess of encoding the coding target block ends (step S628).

A technique for designing the 1D transform matrix A and the 1D transformmatrix B will be described below. According to H.264, nine types ofprediction modes are defined for the 4×4 pixel block and the 8×8 pixelblock. Four types of prediction modes are defined for the 16×16 pixelblock.

First, the prediction error 119 for each prediction mode is generated.Those of the prediction errors 119 for the respective prediction modesare collected which exhibit, in the vertical direction or the horizontaldirection, the above-described tendency to have an absolute valueincreasing with the distance from the reference pixel. Then, singularvalue decomposition is carried out on a matrix in which the directionwith the tendency exhibited therein is defined as a column direction andin which the prediction errors 119 are arranged in a row direction.Thus, a 1D orthogonal basis is designed which eliminates the verticalcorrelation in the matrix. The 1D orthogonal basis is arranged in thecolumn direction as row vectors to generate the 1D transform matrix A.

On the other hand, singular value decomposition is carried out on amatrix in which the direction with the tendency not exhibited therein isdefined as the column direction and in which the prediction errors 119are arranged in the row direction. Thus, a 1D orthogonal basis isgenerated which eliminates the vertical correlation in the matrix. The1D orthogonal basis is arranged in the column direction as row vectorsto generate the 1D transform matrix B. The 1D transform matrix B maysimply be replaced with a matrix for DCT. For simplification, the designfor the 4×4 pixel block has been illustrated. However, 1D transformmatrices for the 8×8 pixel block and the 16×16 pixel block can similarlybe designed. Furthermore, the above-described design technique isillustrative and the design may be carried out as appropriate with theabove-described nature of a prediction error taken into account.

A specific design technique for the 2D-1D transformation for eachprediction mode (scan order) as illustrated in FIG. 9 will be describedbelow. The scan order for each prediction mode can be designed based onthe quantized transform coefficients 121 generated by the quantizationunit 103. For example, the design for the 4×4 pixel block prepares aplurality of training images to generate a prediction error 119 for eachof the nine types of prediction modes. The orthogonal transformationsshown in Expression (3) and Expression (4) are carried out on each ofthe prediction error 119 to generate the transform coefficients 120.Then the transform coefficients 120 are quantized. In connection withthe quantized transform coefficients 121, the number of occurrences ofnonzero coefficients is cumulatively added for each of the elements ofthe 4×4 pixel block. The cumulative addition is carried out on all thetraining images to create a histogram indicative of the occurrencefrequency of nonzero coefficients for each of the 16 elements of the 4×4pixel block. Based on the histogram, indices of 0 to 15 are assigned tothe elements in order of decreasing occurrence frequency. Suchassignment of the indices is individually carried out on all theprediction modes. The order of the assigned indices is used as the scanorder corresponding to each prediction mode.

For simplification, the design for the 4×4 pixel block has beenillustrated. However, the scan orders for the 8×8 pixel block and the16×16 pixel block can similarly be designed. Furthermore, even if thenumber of prediction modes is increased to 17, 33, or any other value,the design can be achieved using a similar technique. The method fordynamically updating the scan order is as described with reference toFIG. 5B.

A syntax utilized by the image encoding apparatus in FIG. 1 will bedescribed.

The syntax is indicative of the structure of encoded data (for example,the encoded data 130 in FIG. 1) obtained by the image encoding apparatusencoding video data. When the encoded data is decoded, the imagedecoding apparatus references the same syntax structure to interpret thesyntax. FIG. 11 illustrates syntax 700 utilized by the image encodingapparatus in FIG. 1.

The syntax 700 includes three parts, that is, high-level syntax 701,slice-level syntax 702, and coding tree-level syntax 703. The high-levelsyntax 701 includes syntax information on a layer higher than a slice.The slice refers to a rectangular area or a continuous area included ina frame or a field. The slice-level syntax 702 includes informationrequired to decode each slice. The coding tree-level syntax 703 includesinformation required to decode each coding tree (that is, each codingtree unit). Each of these parts includes a further detailed syntax.

The high-level syntax 701 includes sequence-level syntax andpicture-level syntax such as sequence parameter set syntax 704 andpicture parameter set syntax 705. The slice-level syntax 702 includesslice header syntax 706 and slice data syntax 707. The coding tree levelsyntax 703 includes coding tree unit syntax 708 and prediction unitsyntax 709.

The coding tree unit syntax 708 may have a quadtree structure.Specifically, as a syntax element of the coding tree unit syntax 708,the coding tree unit syntax 708 can further be recursively invoked. Thatis, one coding tree unit can be divided into pieces using quadtrees.Furthermore, the coding tree unit syntax 708 contains transform unitsyntax 710. The transform unit syntax 710 is invoked at each coding treeunit syntax 708 located at the terminal of the quadtree. The transformunit syntax 710 has information on inverse orthogonal transformation,quantization, and the like described therein.

FIG. 12 illustrates the slice header syntax 706 according to the presentembodiment. slice_directional_unified_transform_flag shown in FIG. 12is, for example, a syntax element which indicates whether the orthogonaltransformation and inverse orthogonal transformation according to thepresent embodiment are enable or disable for a certain slice.

slice_directional_unified_transform_flag of 0 means that the orthogonaltransformation and inverse orthogonal transformation according to thepresent embodiment are enable in the slice. Hence, the orthogonaltransformation unit 102 and the inverse orthogonal transformation unit105 carry out fixed orthogonal transformation and inverse orthogonaltransformation such as DCT and IDCT. The fixed orthogonal transformationand inverse orthogonal transformation may be carried out by the 1Dorthogonal transformation unit B 207, the 1D orthogonal transformationunit B 209, the 1D inverse orthogonal transformation unit B307, and the1D inverse orthogonal transformation unit B309 (that is, by the 1Dtransform matrix B) or by the DCT unit and IDCT unit (neither of theunits is shown in the drawings). Furthermore, the coefficient ordercontrol unit 113 carries out fixed 2D-1D transformation (for example,the zigzag scan). The fixed 2D-1D transformation may be carried out bythe 2D-1D transformation unit (mode 2) 504 or by a 2D-1D transformationunit not shown in the drawings.

By way of example, slice_directional_unified_transform_flag of 1 meansthat the orthogonal transformation and inverse orthogonal transformationaccording to the present embodiment are enable throughout the slice.That is, the encoding process is carried out in accordance with theabove-described flowchart of encoding in FIG. 10A and FIG. 10B. That is,the selection switch 201 selects the 1D orthogonal transformation unit A206 or the 1D orthogonal transformation unit B 207 based on the 1Dtransform matrix set information 129. The selection switch 204 selectsthe 1D orthogonal transformation unit A 208 or the 1D orthogonaltransformation unit B 209 based on the 1D transform matrix setinformation 129. Furthermore, the selection switch 301 selects the 1Dinverse orthogonal transformation unit A 306 or the 1D inverseorthogonal transformation unit B 307 based on the 1D transform matrixset information 129. The selection switch 304 selects the 1D inverseorthogonal transformation unit A 308 or the 1D inverse orthogonaltransformation unit B 309 based on the 1D transform matrix setinformation 129. Moreover, the selection switch 501 selects one of the2D-1D transformation units 502, . . . , and 510 in accordance with theprediction mode information included in the prediction information 126.

Furthermore, in another example, ifslice_directional_unified_transform_flag is 1, a syntax in a lower layer(such as the coding tree unit or the transform unit) may be specified toindicate whether the orthogonal transformation and inverse orthogonaltransformation according to the present embodiment are enable or disablefor each local area inside the slice.

FIG. 13 illustrates the coding tree unit syntax 708 according to thepresent embodiment. ctb_directional_unified_transform_flag shown in FIG.13 is a syntax element indicating whether the orthogonal transformationand inverse orthogonal transformation according to the presentembodiment are enable or disable for a certain coding unit. Furthermore,pred_mode shown in FIG. 13 is a syntax element included in theprediction unit syntax 709 and indicates the type of coding in thecoding tree unit or a macro block. MODE_INTRA indicates that the codingtype is intra-prediction. ctb_directional_unified_transform_flag isencoded only when the above-describedslice_directional_unified_transform_flag is 1 and when the coding typeof the coding tree unit is intra-prediction.

ctb_directional_unified_transform_flag of 0 means that the orthogonaltransformation and inverse orthogonal transformation according to thepresent embodiment are disable in the coding tree unit. Hence, theorthogonal transformation unit 102 and the inverse orthogonaltransformation unit 105 carry out fixed orthogonal transformation andinverse orthogonal transformation such as DCT and IDCT. The fixedorthogonal transformation and inverse orthogonal transformation may becarried out by the 1D orthogonal transformation unit B 207, the 1Dorthogonal transformation unit B 209, the 1D inverse orthogonaltransformation unit B 307, and the 1D inverse orthogonal transformationunit B 309 (that is, by the 1D transform matrix B) or by the DCT unitand IDCT unit (neither of the units is shown in the drawings).Furthermore, the coefficient order control unit 113 carries out fixed2D-1D transformation (for example, the zigzag scan). The fixed 2D-1Dtransformation may be carried out by the 2D-1D transformation unit (mode2) 504 or by the 2D-1D transformation unit not shown in the drawings.

On the other hand, ctb_directional_unified_transform_flag of 1 makes theorthogonal transformation and inverse orthogonal transformationaccording to the present embodiment enable in the coding unit. Then, theencoding process is carried out in accordance with the above-describedflowchart of encoding in FIG. 10A and FIG. 10B. That is, the selectionswitch 201 selects the 10 orthogonal transformation unit A 206 or the 1Dorthogonal transformation unit B 207 based on the 1D transform matrixset information 129. The selection switch 204 selects the 1D orthogonaltransformation unit A 208 or the 1D orthogonal transformation unit B 209based on the 1D transform matrix set information 129. Furthermore, theselection switch 301 selects the 1D inverse orthogonal transformationunit A 306 or the 1D inverse orthogonal transformation unit B 307 basedon the 1D transform matrix set information 129. The selection switch 304selects the 1D inverse orthogonal transformation unit A 308 or the 1Dinverse orthogonal transformation unit B 309 based on the 1D transformmatrix set information 129. Moreover, the selection switch 501 selectsone of the 2D-1D transformation units 502, . . . , and 510 in accordancewith the prediction mode information included in the predictioninformation 126.

When the flag specifying whether the orthogonal transformation andinverse orthogonal transformation according to the present embodimentare enable or disable is encoded in the coding tree unit syntax 708 asin the example in FIG. 13, the amount of information (the amount ofcode) is increased compared to when the flag is not encoded. However,encoding the flag enables the optimum orthogonal transformation to becarried out for each local area (that is, for each coding tree unit).

FIG. 14 illustrates the transform unit syntax 710 according to thepresent embodiment. tu_directional_unified_transform_flag shown in FIG.14 is a syntax element indicating whether the orthogonal transformationand inverse orthogonal transformation according to the presentembodiment are enable or disable for a certain transform unit.Furthermore, pred_mode shown in FIG. 14 is a syntax element included inthe prediction unit syntax 709 and indicates the type of coding in acertain coding tree unit or macro block. MODE_INTRA indicates that thecoding type is intra-prediction. tu_directional_unified_transform_flagis encoded only when the above-describedslice_directional_unified_transform_flag is 1 and when the coding typeof the coding tree unit is intra-prediction.

tu_directional_unified_transform_flag of 0 makes the orthogonaltransformation and inverse orthogonal transformation according to thepresent embodiment disable in the transform unit. Hence, the orthogonaltransformation unit 102 and the inverse orthogonal transformation unit105 carry out fixed orthogonal transformation and inverse orthogonaltransformation such as DCT and IDCT. The fixed orthogonal transformationand inverse orthogonal transformation may be carried out by the 1Dorthogonal transformation unit B 207, the 1D orthogonal transformationunit B 209, the 1D inverse orthogonal transformation unit B 307, and the1D inverse orthogonal transformation unit B 309 (that is, by the 1Dtransform matrix B) or by the DCT unit and IDCT unit (neither of theunits is shown in the drawings). Furthermore, the coefficient ordercontrol unit 113 carries out fixed 2D-1D transformation (for example,the zigzag scan). The fixed 2D-1D transformation may be carried out bythe 2D-1D transformation unit (mode 2) 504 or by the 2D-1Dtransformation unit not shown in the drawings.

On the other hand, tu_directional_unified_transform_flag of 1 makes theorthogonal transformation and inverse orthogonal transformationaccording to the present embodiment enable in the transform unit. Then,the encoding process is carried out in accordance with theabove-described flowchart of encoding in FIG. 10A and FIG. 10B. That is,the selection switch 201 selects the 1D orthogonal transformation unit A206 or the 1D orthogonal transformation unit B 207 based on the 1Dtransform matrix set information 129. The selection switch 204 selectsthe 1D orthogonal transformation unit A 208 or the 1D orthogonaltransformation unit B 209 based on the 1D transform matrix setinformation 129. Furthermore, the selection switch 301 selects the 1Dinverse orthogonal transformation unit A 306 or the 1D inverseorthogonal transformation unit B 307 based on the 1D transform matrixset information 129. The selection switch 304 selects the 1D inverseorthogonal transformation unit A 308 or the 1D inverse orthogonaltransformation unit B 309 based on the 1D transform matrix setinformation 129. Moreover, the selection switch 501 selects one of the2D-1D transformation units 502, . . . , and 510 in accordance with theprediction mode information included in the prediction information 126.

When the flag specifying whether the orthogonal transformation andinverse orthogonal transformation according to the present embodimentare enable or disable is encoded in the transform unit syntax 710 as inthe example in FIG. 14, the amount of information (the amount of code)is increased compared to when the flag is not coded. However, encodingthe flag enables the optimum orthogonal transformation to be carried outfor each local area (that is, for each transform unit).

Syntax elements not specified according to the present embodiment ordescriptions of other conditional branches may be inserted between rowsin the syntax tables illustrated in FIG. 12, FIG. 13, and FIG. 14.Furthermore, the syntax table may be divided into a plurality of tablesor a plurality of the syntax tables may be unified. Additionally, theillustrated terms for the syntax elements may be optionally changed.

As described above, the image encoding apparatus according to thepresent embodiment utilizes the tendency of the intra-prediction to havea prediction accuracy decreasing with increasing distance from thereference pixel. The image encoding apparatus classifies the verticaland horizontal directions of the prediction modes into two classesdepending on whether or not the tendency is present. The image encodingapparatus further adaptively applies the 1D transform matrix A or the 1Dtransform matrix B to each of the vertical and horizontal directions.The 1D transform matrix A is generated by pre-designing a commontransform basis so as to increase the coefficient density after 1Dorthogonal transformation (that is, to reduce the rate of nonzerocoefficients in the quantized transform coefficients 121) in a directionorthogonal to the line of the group of reference pixels (verticaldirection or horizontal direction). On the other hand, the 1D transformmatrix B is generated by designing a general-purpose transform matrixhaving no such nature. For example, the general-purpose transformationis DCT. Hence, the image encoding apparatus according to the presentembodiment achieves a high transform efficiency compared to the casewhere a fixed orthogonal transformation such as DCT is uniformly appliedto the prediction modes.

Furthermore, the orthogonal transformation unit 102 and inverseorthogonal transformation unit 105 according to the present embodimentare suited both for hardware implementation and for softwareimplementation.

Expression (3) to Expression (6) express multiplications of fixedmatrices. Thus, when the orthogonal transformation unit and the inverseorthogonal transformation unit are implemented by hardware, theimplementation is expected to be configured using hard wired logicinstead of multipliers.

If a dedicated transform basis is used for each of the nine types ofintra-prediction modes to carry out orthogonal transformation andinverse orthogonal transformation, nine 2D orthogonal transformationunits need to be prepared or 18 (=9×2) 1D orthogonal transformationunits need to be prepared as shown in FIG. 15. The nine 2D orthogonaltransformation units or 18 1D orthogonal transformation units carry outmultiplications of different transform matrices. As a result, besidesdedicated hardware for DCT required for H.264, the nine 2D orthogonaltransformation units or 18 1D orthogonal transformation units areadditionally provided. This increases the scale of relevant circuits.

On the other hand, as shown in FIG. 2 and FIG. 3, the orthogonaltransformation unit and inverse orthogonal transformation unit accordingto the present embodiment use a combination of two (if a vertical(inverse) transformation unit and a horizontal (inverse) transformationunit are shared in a time division manner) 1D orthogonal transformationunits with a circuit for matrix transposition to carry out four types oftwo-dimensional orthogonal transformations. Hence, the orthogonaltransformation unit and inverse orthogonal transformation unit accordingto the present embodiment allow an increase in the circuit scale in thehardware implementation to be significantly suppressed.

Furthermore, if a dedicated transform basis is used for each of the ninetypes of intra-prediction modes to carry out orthogonal transformationand inverse orthogonal transformation, the software implementation isexpected to be as follows. Nine 2D orthogonal transform matrices or 18(=9×2) 1D orthogonal transform matrices are saved in a memory. Each ofthe transform matrices is invoked for the corresponding one of theprediction modes, and an orthogonal transformation is implemented usinga general-purpose multiplier. This may increase the size of the memoryto which the transform matrices are saved and thus the costs and alsoincrease memory bandwidth as a result of loading of a transform matrixinto the memory for each transformation.

On the other hand, the orthogonal transformation unit and inverseorthogonal transformation unit according to the present embodimentcombines vertical transformation and horizontal transformation using two1D orthogonal transform matrices, to carry out four types of orthogonaltransformations. Thus, the orthogonal transformation unit and inverseorthogonal transformation unit according to the present embodimentallows an increase in the memory size in the software implementation tobe significantly suppressed.

Furthermore, preparing individual scan orders for the respectiveprediction modes as described in the present embodiment contributes toimproving the coding efficiency. The quantized transform coefficients121 shows the tendency to generate nonzero coefficients is biaseddepending on the element. The tendency to generate nonzero coefficientsvaries depending on the prediction direction of the intra-prediction.Moreover, with the same prediction direction, even the encoding of pixelblocks from different input images 118 leads to similar tendencies togenerate nonzero coefficients. Hence, when the coefficient order controlunit 113 transforms the elements into the respective one-dimensionalquantized transform coefficient sequences 122 in order of decreasingoccurrence probability of nonzero coefficients in the quantizedtransform coefficients 121, the nonzero coefficients are very likely todensely occur in the quantized transform coefficient sequence 122. Thisenables a reduction in the amount of code generated as a result of runlength coding in the entropy encoding unit 114. As described withreference to FIG. 5A and FIG. 5B, the coefficient order control unit 113may fixedly utilize scan orders learned for the respective predictionmodes or utilize a scan order dynamically updated during the encodingprocess. Utilizing the scan orders optimized for the respectiveprediction modes, the entropy encoding unit 114 can reduce, compared toH.264, the amount of generated code based on the quantized transformcoefficient sequence 122 without significantly increasing the amount ofcalculation.

Second Embodiment

An image encoding apparatus according to a second embodiment isdifferent from the image encoding apparatus according to the firstembodiment in the details of the orthogonal transformation and theinverse orthogonal transformation. The same components of the presentembodiment as the corresponding components of the first embodiment arehereinafter denoted by the same reference numerals, and mainly differentcomponents will be described below. An image decoding apparatuscorresponding to the image encoding apparatus according to the presentembodiment will be described in a fifth embodiment.

Instead of the orthogonal transformation unit 102 illustrated in FIG. 2,the image encoding apparatus according to the present embodimentincludes the orthogonal transformation unit 102 illustrated in FIG. 16.The orthogonal transformation unit 102 in FIG. 16 includes a selectionswitch 801, a vertical transformation unit 802, the transposition unit203, a selection switch 804, and a horizontal transformation unit 805.The vertical transformation unit 802 includes a 1D orthogonaltransformation unit C 806, a 1D orthogonal transformation unit D 807,and a 1D orthogonal transformation unit E 808. The horizontaltransformation unit 805 includes a 1D orthogonal transformation unit C809, a 1D orthogonal transformation unit D 810, and a 1D orthogonaltransformation unit E 811. The order of the vertical transformation unit802 and the horizontal transformation unit 805 is illustrative and maybe reversed.

The 1D orthogonal transformation unit C 806 and the 1D orthogonaltransformation unit C 809 have common functions in that both unitsmultiply an input matrix by a 1D transform matrix C. The 1D orthogonaltransformation unit D 807 and the 1D orthogonal transformation unit D810 have common functions in that both units multiply the input matrixby a 1D transform matrix D. The 1D orthogonal transformation unit E 808and the 1D orthogonal transformation unit E 811 have common functions inthat both units multiply the input matrix by a 1D transform matrix E.

The 1D transform matrix C, 1D transform matrix D, and 1D transformmatrix E according to the present embodiment will be described below.

As described above, the prediction error 119 has a tendency to have anabsolute value increasing with the distance from the reference pixel.The tendency is similarly exhibited regardless of the predictiondirection. However, the prediction error in the DC prediction mode doesnot exhibit the tendency in the vertical direction or the horizontaldirection. The present embodiment utilizes the 1D transform matrix Edescribed below for the DC prediction mode. For the prediction modesother then the DC prediction mode, the present embodiment adaptivelyutilizes the 1D transform matrix C and the 1D transform matrix Ddepending on whether or not the tendency is present, as is the case withthe first embodiment.

Specifically, the 1D transform matrix C can be generated using the samedesign technique as that for the above-described 1D transform matrix A.Furthermore, the 1D transform matrix D can be generated using a designtechnique similar to the design technique for the above-described 1Dtransform matrix B. That is, the 1D transform matrix D can be generatedby carrying out the design technique for the 1D transform matrix B withthe DC prediction mode excluded.

The 1D transform matrix E may be a matrix for DCT. Alternatively, the 1Dtransform matrix E may be generated by pre-designing a common transformbasis so as to increase, compared to the 1D transform matrix D, thecoefficient density after 1D orthogonal transformation (that is, toreduce the rate of nonzero coefficients in the quantized transformcoefficients 121) in the vertical direction and the horizontaldirection.

Instead of the inverse orthogonal transformation unit 105 illustrated inFIG. 3, the image encoding apparatus according to the present embodimentincludes the inverse orthogonal transformation unit 105 illustrated inFIG. 17. The inverse orthogonal transformation unit 105 in FIG. 17includes a selection switch 901, a vertical inverse transformation unit902, the transposition unit 303, a selection switch 904, and ahorizontal inverse transformation unit 905. The vertical inversetransformation unit 902 includes a 1D inverse orthogonal transformationunit C 906, a 1D inverse orthogonal transformation unit D 907, and a 1Dinverse orthogonal transformation unit E 908. The horizontal inversetransformation unit 905 includes a 1D inverse orthogonal transformationunit C 909, a 1D inverse orthogonal transformation unit D 910, and a 1Dinverse orthogonal transformation unit E 911. The order of the verticalinverse transformation unit 902 and the horizontal inversetransformation unit 905 is illustrative and may be reversed.

The 1D inverse orthogonal transformation unit C 906 and the 1D inverseorthogonal transformation unit C 909 have common functions in that bothunits multiply an input matrix by the transposed matrix of the 1Dtransform matrix C. The 1D inverse orthogonal transformation unit D 907and the 1D inverse orthogonal transformation unit D 910 have commonfunctions in that both units multiply the input matrix by the transposedmatrix of the 1D transform matrix D. The 1D inverse orthogonaltransformation unit E 908 and the 1D inverse orthogonal transformationunit E 911 have common functions in that both units multiply the inputmatrix by the transposed matrix of the 1D transform matrix E.

The 1D transform matrix set information 129 according to the presentembodiment generated by the 1D transform matrix set unit 112 will bedescribed below in detail.

The 1D transform matrix set information 129 directly or indirectlyindicates the vertical transform index for selection of a transformmatrix for use in vertical orthogonal transformation and verticalinverse orthogonal transformation and the horizontal transform index forselection of a transform matrix for use in horizontal orthogonaltransformation and horizontal inverse orthogonal transformation. Forexample, the 1D transform matrix set information 129 can be expressed bya transform index (TrasformIdx) shown in FIG. 18D. Reference to thetable in FIG. 18D allows the vertical transform index (VerticalTransform Idx) and the horizontal transform index (Horizontal TransformIdx) to be derived from the transform index.

As shown in FIG. 18B, a vertical transform index of “0” allows selectionof the above-described 1D transform matrix C (1D_Transform_Matrix_C) orthe transposed matrix thereof for vertical orthogonal transformation orvertical inverse orthogonal transformation. On the other hand, avertical transform index of “1” allows selection of the above-described1D transform matrix D (1D_Transform_Matrix_D) or the transposed matrixthereof for vertical orthogonal transformation or vertical inverseorthogonal transformation. Moreover, a vertical transform index of “2”allows selection of the above-described 1D transform matrix E(1D_Transform_Matrix_E) or the transposed matrix thereof for verticalorthogonal transformation or vertical inverse orthogonal transformation.

As shown in FIG. 18C, a horizontal transform index of “0” allowsselection of the 1D transform matrix C (1D_Transform_Matrix_C) or thetransposed matrix thereof for horizontal orthogonal transformation orhorizontal inverse orthogonal transformation. On the other hand, ahorizontal transform index of “1” allows selection of the 1D transformmatrix D (1D_Transform_Matrix_D) or the transposed matrix thereof forhorizontal orthogonal transformation or horizontal inverse orthogonaltransformation. Moreover, a horizontal transform index of “2” allowsselection of the 1D transform matrix E (1D_Transform_Matrix_E) or thetransposed matrix thereof for horizontal orthogonal transformation orhorizontal inverse orthogonal transformation.

Furthermore, FIG. 18A illustrates the index for each (intra-) predictionmode (IntraN×NPredModeIndex), the name thereof (Name ofIntraN×NPredMode), and the corresponding vertical transform index andhorizontal transform index. In FIG. 18A, “N×N” is indicative of the sizeof the prediction target block (N=4, 8, 16, or the like). The size ofthe prediction target block can be expanded to “M×N” (that is,rectangles other than squares).

FIG. 18E is obtained by integrating FIG. 18A and FIG. 18D together andshows the index for each prediction mode, the name of the predictionmode, and the corresponding transform index.

The 1D transform matrix set unit 112 detects the index of the predictionmode in the prediction mode information included in the predictioninformation 126. The 1D transform matrix set unit 112 then generates thecorresponding 1D transform matrix set information 129. The tables shownin FIG. 18A, FIG. 18B, FIG. 18C, FIG. 18D, and FIG. 18E areillustrative. The 1D transform matrix set unit 112 may generate the 1Dtransform matrix set information 129 while avoiding the use of some orall of the tables.

For example, TransformIdx indicative of 0 means that the verticaltransform index indicates 0 and that the horizontal transform indexindicates 0. This means that the 1D transform matrix C is used forvertical orthogonal transformation and that the 1D transform matrix C isused for horizontal orthogonal transformation. These index values alsomean that the transposed matrix of the 1D transform matrix C is used forvertical inverse orthogonal transformation and that the transposedmatrix of the 1D transform matrix C is used for horizontal inverseorthogonal transformation.

TransformIdx indicative of 1 means that the vertical transform indexindicates 0 and that the horizontal transform index indicates 1. Thismeans that the 1D transform matrix C is used for vertical orthogonaltransformation and that the 1D transform matrix D is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix C is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix D is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 2 means that the vertical transform indexindicates 1 and that the horizontal transform index indicates 0. Thismeans that the 1D transform matrix D is used for vertical orthogonaltransformation and that the 1D transform matrix C is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix D is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix C is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 3 means that the vertical transform indexindicates 2 and that the horizontal transform index indicates 2. Thismeans that the 1D transform matrix E is used for vertical orthogonaltransformation and that the 1D transform matrix E is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix E is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix E is used for horizontal inverse orthogonaltransformation.

Here, if the prediction target block is a rectangular block expressed asM×N, the size of the block to be orthogonally transformed may also beM×N.

The table shown in FIG. 18A assigns the 1D transform matrix setinformation 129 taking the above-described tendency of eachintra-prediction mode into account. That is, for the DC prediction mode,2 is assigned both to the vertical transform index and to the horizontaltransform index. Hence, for the DC prediction mode, the orthogonaltransformation and inverse orthogonal transformation are carried out inthe vertical direction and the horizontal direction using the 1Dtransform matrix E and the transposed matrix thereof. As a result, ahigh transform efficiency is achieved.

For the prediction modes other than the DC prediction mode, 0 isassigned to the vertical transform index if the tendency is exhibited inthe vertical direction of the prediction error. 0 is assigned to thehorizontal transform index if the tendency is exhibited in thehorizontal direction of the prediction error. On the other hand, 1 isassigned to each of the directions not exhibiting the tendency. A hightransform efficiency is achieved by classifying the vertical andhorizontal directions of the prediction modes other than the DCprediction mode into two classes depending whether or not the tendencyis present and adaptively applying the 1D transform matrix C or the 1Dtransform matrix D to each of the vertical and horizontal directions.

As described above, the image encoding apparatus according to thepresent embodiment utilizes the tendency of the intra-prediction to havea decreasing prediction accuracy with increasing distance from thereference pixel as in the case of the first embodiment, while applyingthe orthogonal transformation and the inverse orthogonal transformationto the DC prediction in a manner different from the manner for the otherprediction modes. The image encoding apparatus classifies the verticaland horizontal directions of the prediction modes into the two classesdepending whether or not the tendency is present and adaptively appliesthe 1D transform matrix C or the 1D transform matrix D to each of thevertical and horizontal directions. The image encoding apparatus appliesthe 1D transform matrix E to the DC prediction mode. The 1D transformmatrix C is generated by pre-designing a common transform basis so as toincrease the coefficient density after 1D orthogonal transformation(that is, to reduce the rate of nonzero coefficients in the quantizedtransform coefficients 121) in the direction orthogonal to the line ofthe group of reference pixels (vertical direction or horizontaldirection). The 1D transform matrix D is generated by designing ageneral-purpose transform matrix having no such nature with the DCprediction mode excluded. The 1D transform matrix E may be a matrix forDCT. Alternatively, the 1D transform matrix E is generated bypre-designing a common transform basis so as to increase, for theprediction error 119 in the DC prediction mode, the coefficient densityafter 1D orthogonal transformation (that is, to reduce the rate ofnonzero coefficients in the quantized transform coefficients 121) in thevertical direction and the horizontal direction. Hence, the imageencoding apparatus according to the present embodiment achieves a highertransform efficiency than in the case where fixed orthogonaltransformation such as DCT is uniformly applied to the prediction modes.

Third Embodiment

An image encoding apparatus according to a third embodiment is differentfrom the image encoding apparatuses according to the first embodimentand the second embodiment in the details of the orthogonaltransformation and the inverse orthogonal transformation. The samecomponents of the present embodiment as the corresponding components ofthe first embodiment or the second embodiment are hereinafter denoted bythe same reference numerals, and mainly different components will bedescribed below. An image decoding apparatus corresponding to the imageencoding apparatus according to the present embodiment will be describedin a sixth embodiment.

Instead of the orthogonal transformation unit 102 illustrated in FIG. 2,the image encoding apparatus according to the present embodimentincludes the orthogonal transformation unit 102 illustrated in FIG. 19.The orthogonal transformation unit 102 in FIG. 19 includes a selectionswitch 1201, a vertical transformation unit 1202, the transposition unit203, a selection switch 1204, and a horizontal transformation unit 1205.The vertical transformation unit 1202 includes a 1D orthogonaltransformation unit F 1206, a 1D orthogonal transformation unit G 1207,and a 1D orthogonal transformation unit H 1208. The horizontaltransformation unit 1205 includes a 1D orthogonal transformation unit F1209, a 1D orthogonal transformation unit G 1210, and a 1D orthogonaltransformation unit H 1211. The order of the vertical transformationunit 1202 and the horizontal transformation unit 1205 is illustrativeand may be reversed.

The 1D orthogonal transformation unit F 1206 and the 1D orthogonaltransformation unit F 1209 have common functions in that both unitsmultiply an input matrix by a 1D transform matrix F. The 1D orthogonaltransformation unit G 1207 and the 1D orthogonal transformation unit G1210 have common functions in that both units multiply the input matrixby a 1D transform matrix G. The 1D orthogonal transformation unit H 1208and the 1D orthogonal transformation unit H 1211 have common functionsin that both units multiply the input matrix by a 1D transform matrix H.

The 1D transform matrix F, 1D transform matrix G, and 1D transformmatrix H according to the present embodiment will be described below.

As described above, the prediction error 119 has a tendency to have anabsolute value increasing with the distance from the reference pixel.The tendency is similarly exhibited regardless of the predictiondirection. However, the intra-prediction modes include prediction modesin which only the group of reference pixels on a line located to theleft of and adjacent to the prediction target block or on a line locatedabove and adjacent to the prediction target block is referenced (thereference pixel values are copied or interpolation is carried out usingthe reference pixel values) and prediction modes in which the groups ofreference pixels on the line located to the left of and adjacent to theprediction target block and on the line located above and adjacent tothe prediction target block are referenced. The manner in which thetendency is exhibited varies between the prediction mode for which onlythe group of reference pixels on one line is referenced and theprediction mode for which the groups of reference pixels on two linesare referenced. Thus, the present embodiment carries out orthogonaltransformation and inverse orthogonal transformation differently betweenthe prediction modes in which only the group of reference pixels on oneline is referenced and the prediction modes in which the groups ofreference pixels on two lines are referenced. Specifically, the 1Dtransform matrix H described below is utilized for the prediction modesin which the groups of reference pixels on two lines are referenced. Onthe other hand, the 1D transform matrix F and the 1D transform matrix Gare adaptively utilized for the prediction modes in which only the groupof reference pixels on one line is referenced, depending on whether ornot the tendency is present as is the case with the first embodiment.

Specifically, the 1D transform matrix F can be generated using a designtechnique similar to the design technique for the above-described 1Dtransform matrix A. Furthermore, the 1D transform matrix F can begenerated by carrying out the design technique for the above-described1D transform matrix A while excluding the prediction modes in which thegroups of reference pixels on two lines are referenced (for example, themode 4, mode 5, and mode 6 in FIG. 7A). Furthermore, the 1D transformmatrix G can be generated using the same design technique as that forthe above-described 1D transform matrix B. Alternatively, the 1Dtransform matrix G may be a matrix for DCT.

The 1D transform matrix H may be generated by pre-designing a commontransform basis so as to increase, for the prediction error 119 in theprediction modes in which the groups of reference pixels on two linesare referenced, the coefficient density after 1D orthogonaltransformation (that is, to reduce the rate of nonzero coefficients inthe quantized transform coefficients 121) in the vertical direction andthe horizontal direction.

Instead of the inverse orthogonal transformation unit 105 illustrated inFIG. 3, the image encoding apparatus according to the present embodimentincludes the inverse orthogonal transformation unit 105 illustrated inFIG. 20. The inverse orthogonal transformation unit 105 in FIG. 20includes a selection switch 1301, a vertical inverse transformation unit1302, the transposition unit 303, a selection switch 1304, and ahorizontal inverse transformation unit 1305. The vertical inversetransformation unit 1302 includes a 1D inverse orthogonal transformationunit F 1306, a 1D inverse orthogonal transformation unit G 1307, and a1D inverse orthogonal transformation unit H 1308. The horizontal inversetransformation unit 1305 includes a 1D inverse orthogonal transformationunit F 1309, a 1D inverse orthogonal transformation unit G 1310, and a1D inverse orthogonal transformation unit H 1311. The order of thevertical inverse transformation unit 1302 and the horizontal inversetransformation unit 1305 is illustrative and may be reversed.

The 1D inverse orthogonal transformation unit F 1306 and the 1D inverseorthogonal transformation unit F 1309 have common functions in that bothunits multiply an input matrix by the transposed matrix of the 1Dtransform matrix F. The 1D inverse orthogonal transformation unit G 1307and the 1D inverse orthogonal transformation unit G 1310 have commonfunctions in that both units multiply the input matrix by the transposedmatrix of the 1D transform matrix G. The 1D inverse orthogonaltransformation unit H 1308 and the 1D inverse orthogonal transformationunit H 1311 have common functions in that both units multiply the inputmatrix by the transposed matrix of the 1D transform matrix H.

The 1D transform matrix set information 129 according to the presentembodiment generated by the 1D transform matrix set unit 112 will bedescribed below in detail.

The 1D transform matrix set information 129 directly or indirectlyindicates the vertical transform index for selection of a transformmatrix for use in vertical orthogonal transformation and verticalinverse orthogonal transformation and the horizontal transform index forselection of a transform matrix for use in horizontal orthogonaltransformation and horizontal inverse orthogonal transformation. Forexample, the 1D transform matrix set information 129 can be expressed bya transform index (TrasformIdx) shown in FIG. 21D. Reference to thetable in FIG. 21D allows the vertical transform index (VerticalTransform Idx) and the horizontal transform index (Horizontal TransformIdx) to be derived from the transform index.

As shown in FIG. 21B, a vertical transform index of “0” allows selectionof the above-described 1D transform matrix F (1D_Transform_Matrix_F) orthe transposed matrix thereof for vertical orthogonal transformation orvertical inverse orthogonal transformation. On the other hand, avertical transform index of “1” allows selection of the above-described1D transform matrix G (1D_Transform_Matrix_G) or the transposed matrixthereof for vertical orthogonal transformation or vertical inverseorthogonal transformation. Moreover, a vertical transform index of “2”allows selection of the above-described 1D transform matrix H(1D_Transform_Matrix_H) or the transposed matrix thereof for verticalorthogonal transformation or vertical inverse orthogonal transformation.

As shown in FIG. 21C, a horizontal transform index of “0” allowsselection of the 1D transform matrix F (1D_Transform_Matrix_F) or thetransposed matrix thereof for horizontal orthogonal transformation orhorizontal inverse orthogonal transformation. On the other hand, ahorizontal transform index of “1” allows selection of the 1D transformmatrix G (1D_Transform_Matrix_G) or the transposed matrix thereof forhorizontal orthogonal transformation or horizontal inverse orthogonaltransformation. Moreover, a horizontal transform index of “2” allowsselection of the 1D transform matrix H (1D_Transform_Matrix_H) or thetransposed matrix thereof for horizontal orthogonal transformation orhorizontal inverse orthogonal transformation.

Furthermore, FIG. 21A illustrates the index for each (intra-) predictionmode (IntraN×NPredModeIndex), the name thereof (Name ofIntraN×NPredMode), and the corresponding vertical transform index andhorizontal transform index. In FIG. 21A, “N×N” is indicative of the sizeof the prediction target block (N=4, 8, 16, or the like). The size ofthe prediction target block can be expanded to “M×N” (that is,rectangles other than squares).

FIG. 21E is obtained by integrating FIG. 21A and FIG. 21D together andshows the index for each prediction mode, the name of the index, and thecorresponding transform index.

The 1D transform matrix set unit 112 detects the index of the predictionmode in the prediction mode information included in the predictioninformation 126. The 1D transform matrix set unit 112 then generates thecorresponding 1D transform matrix set information 129. The tables shownin FIG. 21A, FIG. 21B, FIG. 21C, FIG. 21D, and FIG. 21E areillustrative. The 1D transform matrix set unit 112 may generate the 1Dtransform matrix set information 129 while avoiding the use of some orall of the tables.

For example, TransformIdx indicative of 0 means that the verticaltransform index indicates 2 and that the horizontal transform indexindicates 2. This means that the 1D transform matrix H is used forvertical orthogonal transformation and that the 1D transform matrix H isused for horizontal orthogonal transformation. These index values alsomean that the transposed matrix of the 1D transform matrix H is used forvertical inverse orthogonal transformation and that the transposedmatrix of the 1D transform matrix H is used for horizontal inverseorthogonal transformation.

TransformIdx indicative of 1 means that the vertical transform indexindicates 0 and that the horizontal transform index indicates 1. Thismeans that the 1D transform matrix F is used for vertical orthogonaltransformation and that the 1D transform matrix G is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix F is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix G is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 2 means that the vertical transform indexindicates 1 and that the horizontal transform index indicates 0. Thismeans that the 1D transform matrix G is used for vertical orthogonaltransformation and that the 1D transform matrix F is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix G is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix F is used for horizontal inverse orthogonaltransformation.

TransformIdx indicative of 3 means that the vertical transform indexindicates 1 and that the horizontal transform index indicates 1. Thismeans that the 1D transform matrix G is used for vertical orthogonaltransformation and that the 1D transform matrix G is used for horizontalorthogonal transformation. These index values also mean that thetransposed matrix of the 1D transform matrix G is used for verticalinverse orthogonal transformation and that the transposed matrix of the1D transform matrix G is used for horizontal inverse orthogonaltransformation.

Here, if the prediction target block is a rectangular block expressed asM×N, the size of the block to be orthogonally transformed may also beM×N.

The table shown in FIG. 21A assigns the 1D transform matrix setinformation 129 taking the above-described tendency of eachintra-prediction mode into account. That is, for the prediction modes inwhich the groups of reference pixels on two lines are referenced, 2 isassigned both to the vertical transform index and to the horizontaltransform index. Hence, for the prediction modes in which the groups ofreference pixels on two lines are referenced, the orthogonaltransformation and inverse orthogonal transformation are carried out inthe vertical direction and the horizontal direction using the 1Dtransform matrix H and the transposed matrix thereof. As a result, ahigh transform efficiency is achieved.

For the prediction modes other than those in which the groups ofreference pixels on two lines are referenced, 0 is assigned to thevertical transform index if the tendency is exhibited in the verticaldirection of the prediction error. 0 is assigned to the horizontaltransform index if the tendency is exhibited in the horizontal directionof the prediction error. On the other hand, 1 is assigned to each of thedirections not exhibiting the tendency. A high transform efficiency isachieved by classifying the vertical and horizontal directions of theprediction modes other than those in which the groups of referencepixels on two lines are referenced, into two classes depending whetheror not the tendency is present, and adaptively applying the 1D transformmatrix F or the 1D transform matrix G to each of the vertical andhorizontal directions.

As described above, the image encoding apparatus according to thepresent embodiment utilizes the tendency of the intra-prediction to havea decreasing prediction accuracy with increasing distance from thereference pixel as in the case of the first embodiment, while applyingthe orthogonal transformation and the inverse orthogonal transformationto the prediction modes in a manner varying depending on the number oflines corresponding to the groups of reference pixels. The imageencoding apparatus classifies the vertical and horizontal directions ofthe prediction modes other than those in which the groups of referencepixels on two lines are referenced, into the two classes dependingwhether or not the tendency is present, and adaptively applies the 1Dtransform matrix F or the 1D transform matrix G to each of the verticaland horizontal directions. On the other hand, the image encodingapparatus applies the 1D transform matrix H to the prediction modes inwhich the groups of reference pixels on two lines are referenced. Forthe prediction modes in which only the group of reference pixels on oneline is referenced, the 1D transform matrix F is generated bypre-designing a common transform basis so as to increase the coefficientdensity after 1D orthogonal transformation (that is, to reduce the rateof nonzero coefficients in the quantized transform coefficients 121) inthe direction orthogonal to the line of the group of reference pixels(vertical direction or horizontal direction). On the other hand, the 1Dtransform matrix G is generated by designing a general-purpose transformmatrix having no such nature. Moreover, the 1D transform matrix H isgenerated by pre-designing a common transform basis so as to increase,for the prediction error 119 in each prediction mode for which the groupof reference pixels on two lines are referenced, the coefficient densityafter 1D orthogonal transformation (that is, to reduce the rate ofnonzero coefficients in the quantized transform coefficients 121) in thevertical direction and the horizontal direction. Hence, the imageencoding apparatus according to the present embodiment achieves a highertransform efficiency than in the case where fixed orthogonaltransformation such as DCT is uniformly applied to the prediction modes.

The first to third embodiments prepare two or three types of 1Dtransform matrices and select one of the 1D transform matrices forvertical transformation (or vertical inverse transformation) andhorizontal transformation (or horizontal inverse transformation)according to the prediction mode. However, the above-described two orthree types of 1D transform matrices are illustrative. The codingefficiency can be improved by preparing more transform matrices. Forexample, the second embodiment and the third embodiment can be combinedtogether to prepare four types of 1D transform matrices. However, anincreased number of types of transform matrices prepared requireadditional hardware and the like. Thus, the balance between the codingefficiency and disadvantages resulting from an increased number of typesof transform matrices desirably needs to be taken into account.

Fourth Embodiment

A fourth embodiment relates to an image decoding apparatus. The imageencoding apparatus corresponding to the image decoding apparatusaccording to the present embodiment is as described in the firstembodiment. That is, the image decoding apparatus according to thepresent embodiment decodes encoded data generated by, for example, theimage encoding apparatus according to the first embodiment.

As shown in FIG. 22, the image decoding apparatus according to thepresent embodiment includes an input buffer 401, an entropy decodingunit 402, a coefficient order control unit 403, a de-quantization unit404, an inverse orthogonal transformation unit 405, an addition unit406, a reference image memory 407, an intra-prediction unit 408, aninter-prediction unit 409, a selection switch 410, a 1D transform matrixset unit 411, and an output buffer 412.

The image decoding apparatus in FIG. 22 decodes encoded data accumulatedin the input buffer 401, accumulates a decoded image 419 in the outputbuffer 412, and outputs the decoded image 419 as an output image 425.The encoded data 414 is output by, for example, the image encodingapparatus in FIG. 1, and temporarily accumulated in the input buffer 401via an accumulation system or a transmission system (not shown in thedrawings).

In order to decode the encoded data 414, the entropy decoding unit 402decodes every frame or field based on syntax. The entropy decoding unit402 subjects each code sequence of the syntax to entropy decoding toreproduce coding parameters for the coding target block such asprediction information 424 including prediction mode information 421 anda quantized transform coefficient sequence 415. The coding parametersare required for decoding and include the prediction information 424,information on transform coefficients, and information on quantization.The quantized transform coefficient sequence 415 is input to thecoefficient order control unit 403. Furthermore, the prediction modeinformation 421, included in the prediction information 424, issimilarly input to the coefficient order control unit 403. Theprediction information 424 is input to the 1D transform matrix set unit411 and the selection switch 410.

The coefficient order control unit 403 transforms the quantizedtransform coefficient sequence 415 which is a one-dimensional expressioninto a quantized transform coefficients 416 which are a two-dimensionalexpression. The coefficient order control unit 403 then inputs thequantized transform coefficients 416 to the de-quantization unit 404.The coefficient order control unit 403 will be described below indetail.

The de-quantization unit 404 de-quantizes the quantized transformcoefficients 416 from the coefficient order control unit 403 to obtain arestored transform coefficients 417. Specifically, the de-quantizationunit 404 carries out de-quantization in accordance with the informationon the quantization decoded by the entropy decoding unit 402. The dquantization unit 404 inputs the restored transform coefficients 417 tothe inverse orthogonal transformation unit 405.

The inverse orthogonal transformation unit 405 carries out an inverseorthogonal transformation corresponding to the orthogonal transformationperformed on the encoding side, on the restored transform coefficients417 from the de-quantization unit 404 to obtain a restored predictionerror 418. The inverse orthogonal transformation unit 405 inputs therestored prediction error 418 to the addition unit 406.

Specifically, the inverse orthogonal transformation unit 405 accordingto the present embodiment is a component which is substantially the sameas or similar to the inverse orthogonal transformation unit 105 in FIG.3 and will thus not be described below in detail. In particular, theinverse orthogonal transformation unit 405 according to the presentembodiment utilizes the 1D transform matrix A and 1D transform matrix Bwhich are common to the inverse orthogonal transformation unit in FIG.3. The restored transform coefficients 122, 1D transform matrix setinformation 129, and restored prediction error 123 in FIG. 3 correspondto the restored transform coefficients 417, 1D transform matrix setinformation 422, and restored prediction error 418 according to thepresent embodiment, respectively.

The addition unit 406 adds the restored prediction error 418 and thecorresponding prediction image 423 together to generate the decodedimage 419. The decoded image 419 is temporarily accumulated in theoutput buffer 412 for the output image 425 and also saved to thereference image memory 407 for a reference image 420. The decoded image419 saved to the reference image memory 407 is referenced in frame orfield units as necessary by the intra-prediction unit 408 and theinter-prediction unit 409 as the reference image 420. The decoded image419 temporarily accumulated in the output buffer 412 is output at anoutput timing managed by the decoding control unit 413.

The intra-prediction unit 408, the inter-prediction unit 409, and theselection switch 410 are components which are substantially the same asor similar to the intra-prediction unit 108, inter-prediction unit 109,and selection switch 110 in FIG. 1 and will thus not be described belowin detail. The decoding control unit 413 controls the components of theimage decoding apparatus in FIG. 22. Specifically, the decoding controlunit 413 performs various control operations for a decoding processincluding the above-described operations.

The 1D transform matrix set unit 411 generates the 1D transform matrixset information 422 based on the prediction mode information included inthe prediction information 424 from the entropy decoding unit 402. The1D transform matrix set unit 411 inputs the 1D transform matrix setinformation 422 to the inverse orthogonal transformation unit 405.

Specifically, the 1D transform matrix set unit 411 is a component whichis substantially the same as or similar to the 1D transform matrix setunit 112 according to the first embodiment and will thus not bedescribed below in detail. That is, the 1D transform matrix set unit 411according to the present embodiment uses, for example, the tables inFIG. 4A, FIG. 4B, FIG. 4C, FIG. 4D, and FIG. 4E to generate the 1Dtransform matrix set information 422. The prediction information 126 and1D transform matrix set information 129 according to the firstembodiment correspond to the prediction information 424 and 1D transformmatrix set information 422 according to the present embodiment,respectively.

Furthermore, the image decoding apparatus in FIG. 22 utilizes a syntaxwhich is the same as or similar to the syntax described with referenceto FIG. 11, FIG. 12, FIG. 13, and FIG. 14. Thus, the detaileddescription of the syntax is omitted.

The coefficient order control unit 403 will be described below indetail.

The coefficient order control unit 403 transforms the quantizedtransform coefficient sequence 415, which is a one-dimensionalexpression, into the quantized transform coefficients 416, which are atwo-dimensional expression, by arranging the elements of the quantizedtransform coefficient sequence 415 in a predetermined order (that is,the order corresponding to the order used on the encoding side). By wayof example, if the encoding side carries out 2D-1D transformationregardless of the prediction mode, the coefficient order control unit403 can perform common 1D-2D transformation regardless of the predictionmode. Specifically, the coefficient order control unit 403 can utilizean inverse zigzag scan as is the case with H.264. The inverse zigzagscan is a 1D-2D transformation corresponding to the above-describedzigzag scan.

In another example, if the encoding side carries out individual 2D-1Dtransformations for the respective prediction modes, the coefficientorder control unit 403 can also perform individual 1D-2D transformationsfor the respective prediction modes. The coefficient order control unit403 performing such an operation is illustrated in FIG. 23A. Thecoefficient order control unit 403 includes a selection switch 1001 andindividual 1D-2D transformation units 1002, . . . , and 1010 for therespective prediction modes. In accordance with the prediction modeinformation (for example, the indices for the prediction modes in FIG.4A) included in the prediction information 424, the selection switch1001 leads the quantized transform coefficient sequence 415 to the 1D-2Dtransformation unit (one of 1002, . . . , and 1010) corresponding to theprediction mode. For example, a prediction mode index of 0 allows theselection switch 1001 to lead the quantized transform coefficientsequence 415 to the 1D-2D transformation unit 1002. In FIG. 23A, theprediction modes and the 1D-2D transformation units are on a one-to-onecorrespondence. The quantized transform coefficient sequence 415 is ledto one 1D-2D transformation unit corresponding to the prediction mode.The quantized transform coefficient sequence 415 is then transformedinto the quantized transform coefficients 416.

In another example, if the encoding side dynamically updates the scanorder in the 2D-1D transformation, the coefficient order control unit403 may also dynamically update the scan order in the 1D-2Dtransformation in a manner corresponding to the manner used on theencoding side. The coefficient order control unit 403 performing such anoperation is illustrated in FIG. 23B. The coefficient order control unit403 includes the selection switch 1001, the individual 1D-2Dtransformation units 1002, . . . , and 1010 for the respective ninetypes of prediction modes, an occurrence frequency count unit 1011, anda coefficient order update unit 1012. The selection switch 1001 is asdescribed with reference to FIG. 23A. The individual 1D-2Dtransformation units 1002, . . . , and 1010 for the respective ninetypes of prediction modes are different from the 1D-2D transformationunits in FIG. 23A in that the scan order for the 1D-2D transformationunits 1002, . . . , and 1010 is updated by the coefficient order updateunit 1012.

The occurrence frequency count unit 1011 creates a histogram of thenumber of occurrences of nonzero coefficients in each element of thequantized transform coefficient sequence 416. The occurrence frequencycount unit 1011 inputs the created histogram 1013 to the coefficientorder update unit 1012.

The coefficient order update unit 1012 updates the order of coefficientsat a predetermined timing based on the histogram 1013. The timing maybe, for example, a timing when a decoding process carried out on acoding tree unit is finished or a timing when a decoding process carriedout on one line in the coding tree unit is finished.

Specifically, the coefficient order control unit 1012 references thehistogram 1013 to update the order of coefficients for a prediction modewith an element for which the counted number of occurrences of nonzerocoefficients is equal to or larger than a threshold. For example, thecoefficient order control unit 1012 performs the updating for aprediction mode with an element for which the counted number ofoccurrences of nonzero coefficients is 16 or more. Setting a thresholdfor the number of occurrences allows the order of coefficients to beglobally updated, thus avoiding convergence to a local optimum solution.

The coefficient order control unit 1012 sorts, for the updating-targetprediction mode, the elements in order of decreasing occurrencefrequency of nonzero coefficients. The sorting can be achieved inaccordance with an existing algorithm, for example, bubble sort or quicksort. The coefficient order control unit 1012 inputs coefficient orderupdate information 1014 indicative of the sorted order of the elementsto the 1D-2D transformation unit corresponding to the updating-targetprediction mode.

Once the coefficient order update information 1014 is input to the 1D-2Dtransformation unit, the 1D-2D transformation unit carries out a 1D-2Dtransformation in accordance with the updated scan order. If the scanorder is dynamically updated, initial scan orders for the 1D-2Dtransform units need to be set which correspond to the scan order on theencoding side.

For simplification, H.264 has been illustrated and the case of the ninetypes of prediction modes has been described. However, even if thenumber of types of the prediction mode is increased to 17, 33, or thelike, the individual 1D-2D transformations for the respective predictionmodes can be achieved by adding 1D-2D transformation units correspondingto the prediction modes resulting from the increase.

As described above, the image decoding apparatus according to thepresent embodiment includes an inverse orthogonal transformation unitwhich is the same as or similar to the inverse orthogonal transformationunit of the image encoding apparatus according to the first embodiment.Hence, the image decoding apparatus according to the present embodimentexerts effects which are the same as or similar to the effects of theimage encoding apparatus according to the first embodiment.

Fifth Embodiment

An image decoding apparatus according to a fifth embodiment is differentfrom the image decoding apparatus according to the fourth embodiment inthe details of the inverse orthogonal transformation. The samecomponents of the present embodiment as the corresponding components ofthe fourth embodiment are hereinafter denoted by the same referencenumerals, and mainly different components will be described below. Theimage encoding apparatus corresponding to the image decoding apparatusaccording to the present embodiment is as described in the secondembodiment.

The inverse orthogonal transformation unit 405 according to the presentembodiment is a component which is substantially the same as or similarto the inverse orthogonal transformation unit 105 in FIG. 17 and willthus not be described below in detail. In particular, the inverseorthogonal transformation unit 405 according to the present embodimentutilizes the 1D transform matrix C, 1D transform matrix D, and 1Dtransform matrix E which are common to the inverse orthogonaltransformation unit 105 in FIG. 17. The restored transform coefficients122, 1D transform matrix set information 129, and restored predictionerror 123 in FIG. 17 correspond to the restored transform coefficients417, the 1D transform matrix set information 422, and a restoredprediction error signal 418 according to the present embodiment,respectively.

The 1D transform matrix set unit 411 according to the present embodimentis a component which is substantially the same as or similar to the 1Dtransform matrix set unit 112 according to the second embodiment andwill thus not described below in detail. That is, the 1D transformmatrix set unit 411 according to the present embodiment utilizes, forexample, the tables in FIG. 18A, FIG. 18B, FIG. 18C, FIG. 18D, and FIG.18E to generate the 1D transform matrix set information 422. Theprediction information 126 and 1D transform matrix set information 129according to the second embodiment correspond to the predictioninformation 424 and 1D transform matrix set information 422 according tothe present embodiment, respectively.

As described above, the image decoding apparatus according to thepresent embodiment includes an inverse orthogonal transformation unitwhich is the same as or similar to the inverse orthogonal transformationunit of the image encoding apparatus according to the second embodiment.Hence, the image decoding apparatus according to the present embodimentexerts effects which are the same as or similar to the effects of theimage encoding apparatus according to the second embodiment.

Sixth Embodiment

An image decoding apparatus according to a sixth embodiment is differentfrom the image decoding apparatuses according to the fourth embodimentand the fifth embodiment in the details of the inverse orthogonaltransformation. The same components of the present embodiment as thecorresponding components of the fourth embodiment or the fifthembodiment are hereinafter denoted by the same reference numerals, andmainly different components will be described below. The image encodingapparatus corresponding to the image decoding apparatus according to thepresent embodiment is as described in the third embodiment.

The inverse orthogonal transformation unit 405 according to the presentembodiment is a component which is substantially the same as or similarto the inverse orthogonal transformation unit 105 in FIG. 20 and willthus not be described below in detail. In particular, the inverseorthogonal transformation unit 405 according to the present embodimentutilizes the 1D transform matrix F, 1D transform matrix G, and 1Dtransform matrix H which are common to the inverse orthogonaltransformation unit 105 in FIG. 20. The restored transform coefficients122, 1D transform matrix set information 129, and restored predictionerror 123 in FIG. 20 correspond to the restored transform coefficients417, 1D transform matrix set information 422, and restored predictionerror signal 418 according to the present embodiment, respectively.

The 1D transform matrix set unit 411 according to the present embodimentis a component which is substantially the same as or similar to the 1Dtransform matrix set unit 112 according to the third embodiment and willthus not described below in detail. That is, the 1D transform matrix setunit 411 according to the present embodiment utilizes, for example, thetables in FIG. 21A, FIG. 21B, FIG. 21C, FIG. 21D, and FIG. 21E togenerate the 1D transform matrix set information 422. The predictioninformation 126 and 1D transform matrix set information 129 according tothe third embodiment correspond to the prediction information 424 and 1Dtransform matrix set information 422 according to the presentembodiment, respectively.

As described above, the image decoding apparatus according to thepresent embodiment includes an inverse orthogonal transformation unitwhich is the same as or similar to the inverse orthogonal transformationunit of the image encoding apparatus according to the third embodiment.Hence, the image decoding apparatus according to the present embodimentexerts effects which are the same as or similar to the effects of theimage encoding apparatus according to the third embodiment.

The fourth to sixth embodiments prepare two or three types of 1Dtransform matrices and select one of the 1D transform matrices forvertical inverse transformation and horizontal inverse transformationaccording to the prediction mode. However, the above-described two orthree types of 1D transform matrices are illustrative. The codingefficiency can be improved by preparing more transform matrices. Forexample, the fifth embodiment and the sixth embodiment can be combinedtogether to prepare four types of 1D transform matrices. However, anincreased number of types of transform matrices prepared requireadditional hardware and the like. Thus, the balance between the codingefficiency and disadvantages resulting from an increased number of typesof transform matrices desirably needs to be taken into account.

Modifications of the embodiments will be listed and introduced below.

The first to sixth embodiments describe the example in which a frame isdivided into rectangular blocks with a 16×16 pixel size or the like andin which encoding or decoding is carried out on each block in order fromupper left to lower right in the picture (see FIG. 6A). However, theencoding order and the decoding order are not limited to this example.For example, the encoding and decoding may be carried out in order fromlower right to upper left or spirally from the center to the end of thepicture. Moreover, the encoding and decoding may be carried out in orderfrom upper right to lower left or spirally from the end to the center ofthe picture.

The first to sixth embodiments illustrate the prediction target blocksizes such as the 4×4 pixel block, the 8×8 pixel block, and the 16×16pixel size for description. However, the prediction target block neednot necessarily have a uniform block shape. For example, examples of theprediction target block size may include a 16×8 pixel block, an 8×16pixel block, an 8×4 pixel block, or a 4×8 pixel block. Furthermore, notall the blocks within one coding tree unit need to have the same blocksize, and a plurality of different block sizes may be adopted togetherwithin the coding tree unit. If a plurality of different block sizes areadopted together within the coding tree unit, the increased number ofblocks into which the coding tree unit is divided increases the amountof code required to encode or decode division information. Thus, theblock size is desirably selected taking into account the balance betweenthe amount of code for the division information and the quality of thelocal decoded image or decoded image.

For simplification, the first to sixth embodiments comprehensivelydescribe the color signal components without distinguishing luminancesignals from color difference signals. However, if the predictionprocess varies between the luminance signal and the color differencesignal, the same prediction scheme or different prediction schemes maybe used. If different prediction schemes are used for the luminancesignal and for the color difference signal, the prediction schemeselected for the color difference signal can be encoded or decoded in amanner similar to the manner for the luminance signal.

For simplification, the first to sixth embodiments comprehensivelydescribe the color signal components without distinguishing theluminance signal from the color difference signal. However, if theorthogonal transformation process varies between the luminance signaland the color difference signal, the same orthogonal transformationscheme or different orthogonal transformation schemes may be used. Ifdifferent orthogonal transformation schemes are used for the luminancesignal and for the color difference signal, the orthogonaltransformation scheme selected for the color difference signal can beencoded or decoded in a manner similar to the manner for the luminancesignal.

As described above, each of the embodiments achieves efficientorthogonal transformation and inverse orthogonal transformation whilealleviating difficulties in the hardware implementation and the softwareimplementation. Hence, each embodiment improves the coding efficiencyand thus subjective image quality.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the inventions.

For example, a program can be provided which is stored in a computerreadable storage medium and configured to implement the processingaccording to each of the embodiments. The storage medium may be in anystorage format provided that the program can be stored in the storagemedium and read from the storage medium by a computer; the storagemedium may be a magnetic disk, an optical disc (CD-ROM, CD-R, DVD, orthe like), a magneto-optical disk (MO or the like), a semiconductormemory, or the like.

Furthermore, the program configured to implement the processingaccording to each of the embodiments may be stored in a computer(server) connected to a network such as the Internet. Thus, the programmay be downloaded into a computer (client) via the network.

What is claimed is:
 1. An image encoding apparatus comprising: anintra-prediction unit configured to predict a prediction error of atarget image to be encoded based on an intra-prediction mode; a settingunit configured to set a combination of a vertical transform matrix anda horizontal transform matrix corresponding to the target image based ona predetermined relation; a first transforming unit configured totransform the prediction error using the combination of the verticaltransform matrix and the horizontal transform matrix, to obtaintransform coefficients; and an encoding unit configured to encode thetransform coefficients and information indicating the intra-predictionmode for the target image, and wherein the combination comprises any ofa plurality of transform matrices including a first transform matrix anda second transform matrix which increases a coefficient density comparedto the first transform matrix if a one-dimensional orthogonaltransformation in a direction orthogonal to a line of a group ofreference pixels on at least one line is performed on the predictionerror in the intra-prediction mode in which the group of referencepixels is referenced to generate an intra-prediction image.
 2. Theapparatus according to claim 1, wherein the second transform matrixincludes a transform basis pre-designed so as to increase thecoefficient density compared to the first transform matrix if theone-dimensional orthogonal transformation in the direction orthogonal tothe line of the group of reference pixels on at least one line isperformed, based on a tendency to increase an absolute value of theprediction error in the intra-prediction mode in which the group ofreference pixels is referenced to generate the intra-prediction image.3. The apparatus according to claim 1, wherein the setting unit sets thesecond transform matrix to a vertical transform matrix corresponding tothe intra-prediction mode in which the group of reference pixels on atleast one line is referenced to generate the intra-prediction image ifthe line of the group of reference pixels includes a horizontal line,and sets the second transform matrix to a horizontal transform matrixcorresponding to the intra-prediction mode if the line of the group ofreference pixels includes a vertical line.
 4. The apparatus according toclaim 1, further comprising a second transforming unit configured totransform the transform coefficients into a one-dimensional expressionin an individual scan order corresponding to the intra-prediction modefor the target image before the transform coefficients are encoded,wherein the individual scan order corresponding to the intra-predictionmode for the target image is pre-designed to match an order ofdecreasing occurrence frequency of nonzero coefficients in the transformcoefficients of the intra-prediction mode after quantization.
 5. Theapparatus according to claim 4, further comprising an update unitconfigured to dynamically update the individual scan order correspondingto the intra-prediction mode for the target image in such a manner thatthe individual scan order matches order of decreasing occurrencefrequency of nonzero coefficients in the transform coefficients of theintra-prediction mode after quantization.
 6. The apparatus according toclaim 1, wherein the plurality of transform matrices include a thirdtransform matrix which increases the coefficient density compared to thefirst transform matrix if a one-dimensional orthogonal transformation ina vertical direction and a horizontal direction is performed on aprediction error in an intra-prediction mode for a DC prediction.
 7. Theapparatus according to claim 6, wherein the third transform matrix is adiscrete cosine transform matrix.
 8. The apparatus according to claim 1,wherein the second transform matrix increases the coefficient densitycompared to the first transform matrix if the one-dimensional orthogonaltransformation in the direction orthogonal to the line of the group ofreference pixels on one line is performed on the prediction error in theintra-prediction mode in which the group of reference pixels isreferenced to generate the intra-prediction image, and the plurality oftransform matrices include a third transform matrix which increases thecoefficient density compared to the first transform matrix if aone-dimensional orthogonal transformation in a vertical direction and ahorizontal direction is performed on the prediction error in theintra-prediction mode in which the groups of reference pixels on twolines are referenced to generate the intra-prediction image.
 9. An imagedecoding apparatus comprising: a decoding unit configured to decodetransform coefficients for a target image to be decoded and informationindicating an intra-prediction mode for the target image; a setting unitconfigured to set a combination of a vertical inverse transform matrixand a horizontal inverse transform matrix corresponding to the targetimage based on a predetermined relation; an inverse transforming unitconfigured to inversely transform the transform coefficients using thecombination of the vertical inverse transform matrix and the horizontalinverse transform matrix, to obtain a prediction error; and generatingunit configured to generate a decoded image based on the predictionerror, and wherein the combination comprises any of a plurality oftransposed matrices of a plurality of transform matrices including afirst transform matrix and a second transform matrix which increases acoefficient density compared to the first transform matrix if aone-dimensional orthogonal transformation in a direction orthogonal to aline of a group of reference pixels on at least one line is performed onthe prediction error in the intra-prediction mode in which the group ofreference pixels is referenced to generate an intra-prediction image.10. The apparatus according to claim 9, wherein the second transformmatrix includes a transform basis pre-designed so as to increase thecoefficient density compared to the first transform matrix if theone-dimensional orthogonal transformation in the direction orthogonal tothe line of the group of reference pixels on at least one line isperformed, based on a tendency to increase an absolute value of theprediction error in the intra-prediction mode in which the group ofreference pixels is referenced to generate the intra-prediction image.11. The apparatus according to claim 9, wherein the setting unit sets atransposed matrix of the second transform matrix to a vertical inversetransform matrix corresponding to the intra-prediction mode in which thegroup of reference pixels on at least one line is referenced to generatethe intra-prediction image if the line of the group of reference pixelsincludes a horizontal line, and sets the transposed matrix of the secondtransform matrix to a horizontal transform matrix corresponding to theintra-prediction mode if the line of the group of reference pixelsincludes a vertical line.
 12. The apparatus according to claim 9,further comprising transforming unit configured to transform thetransform coefficients into a two-dimensional expression in anindividual scan order corresponding to the intra-prediction mode for thetarget image before the vertical inverse transformation and thehorizontal inverse transformation are performed on the transformcoefficients, wherein the individual scan order corresponding to theintra-prediction mode for the target image is pre-designed to match anorder of decreasing occurrence frequency of nonzero coefficients in thetransform matrix of the intra-prediction mode before de-quantization.13. The apparatus according to claim 12, further comprising an updateunit configured to dynamically update the individual scan ordercorresponding to the intra-prediction mode for the target image in sucha manner that the individual scan order matches the order of decreasingoccurrence frequency of nonzero coefficients in the transformcoefficients of the intra-prediction mode before de-quantization. 14.The apparatus according to claim 9, wherein the plurality of transformmatrices include a third transform matrix which increases thecoefficient density compared to the first transform matrix if aone-dimensional orthogonal transformation in a vertical direction and ahorizontal direction is performed on a prediction error in anintra-prediction mode for a DC prediction.
 15. The apparatus accordingto claim 14, wherein the third transform matrix is a transposed matrixof discrete cosine transform matrix.
 16. The apparatus according toclaim 9, wherein the second transform matrix increases the coefficientdensity compared to the first transform matrix if the one-dimensionalorthogonal transformation in the direction orthogonal to the line of thegroup of reference pixels on one line is performed on the predictionerror in the intra-prediction mode in which the group of referencepixels is referenced to generate the intra-prediction image, and theplurality of transform matrices include a third transform matrix whichincreases the coefficient density compared to the first transform matrixif a one-dimensional orthogonal transformation in a vertical directionand a horizontal direction is performed on the prediction error in theintra-prediction mode in which the groups of reference pixels on twolines are referenced to generate the intra-prediction image.